So what can I do to avoid being "that" passenger with bad hygiene?

Taking regular showers is actually the root cause of this problem. Biologically, taking showers, washing your skin with soap, shampooing your hair, etc. etc. is totally unnatural and it leads to diseases. It destroys your natural skin flora, but far from becoming totally sterile, it causes your skin to get populated by microbes that would normally not be present or not be the dominant microbes. It are these unnatural microbes that will make you smelly if you don’t take a shower for a day.

As pointed out here:

When I was a kid, bathtime was a once-a-week affair. We weren’t an unhygienic family – this is just how most of us lived in the 1960s, and I do not remember any horrific body odours resulting from it. By the time I was an adult, I was showering every day. With hindsight, I should have stuck to the old ways.

The habit of taking regular showers does not only make you prone to become smelly, it causes serious diseases. As pointed out here:

The results were incredible. Like most of us in the Western world, the families had far fewer types of bacteria living in and on them when compared with people in traditional tribes in parts of the developing world. One hunter-gatherer community was found to not only have a higher diversity of bacteria, but only one in 1,500 suffered from an allergy – compared with one in three in the UK.

The detrimental effect of excessive hygiene on the skin flora may affect your gut microbiome, problems there have been linked to not only intestinal diseases, but also heart disease and even Alzheimer’s disease.

We have to take very seriously the fact that we didn’t design the human body, the fact that we take regular showers is not based on any deep insight on how the human body actually works, rather it’s based on ideas that are now known to be totally wrong. If you just kick the habit of taking regular showers, then you’re going to allow your own body to determine what microbes it wants to have on its skin. But it will take a while for this effect to kick in. The more you exercise, the more sweat your body produces, the faster this feedback mechanism will kick in.

If you are able to convert to the no-shower routine, all you need to do is use only moderate amounts of deodorant, probably less than what you use now after taking a shower in the morning on your way to work. Best of all is that sweating will no longer make you a lot more smelly, the effect is quite minimal compared to people who take regular showers.

Lots of options! Starting with the ones that require no forward planning:

• Just lock yourself in the toilets for 10 minutes and wash your… smellier parts using your hands, sink water, soap dispenser soap and the paper towels provided. Yes, it’s not exactly dignified, but no-one’s watching (probably), and it’s more dignified than causing your neighbour to put medieval plague doctor balm under their nose. Bit of water and soap on your hands, push or remove clothing far enough to reach your… various crevices, quick scrub, dry off with paper towels, bin the paper towels. If parents can change and clean babies in those things, you can give yourself a quick scrub

• Ask an attendant if they have disposable wet wipes available, or “hand sanitizer wipes”. Many if not most airlines do, and some even give them to everyone to clean their hands before or after eating (seems to be particularly common in Asia). Even those that don’t do this will often have a small supply available on request: they’re useful for parents, germophobes and people who are ill or travel-sick (as well as the self-consciously sweaty). Then lock yourself in the lav and use them to freshen up. This is a favourite item for “10 things you didn’t know you could ask for on a plane” type list articles:

  If you forget to pack your own sanitizing wipes, ask a flight attendant since they usually have them on hand.

Some more options when you can plan ahead before a long, complicated or hot and bothersome journey, in order of decreasing easiness:

• Bring a spare t-shirt or equivalent, then choose an appropriate point during the journey to change (e.g. between connecting flights, after changing climates, or maybe after sleeping). It’s always a good idea to have some clothes in your hand luggage anyway, in case your checked bags go missing or are delayed
• Bring spare clean socks if you prefer to take your shoes off on long flights and there’s a lot of walking before one of your flights (e.g. it’s an evening flight and you can’t change or shower before heading to the airport)
• Bring a plastic carrier bag or dry bag so that after changing, you can wrap
  your worn clothes up while still locked in the toilet and not stink anyone out while stashing them in your bag

• Bring chewing gum, and/or one of those travel toothbrush/tiny toothpaste sets, often sold at airports, sometimes not unreasonably expensive. For example:

  

• Bring your own pack of wet-wipes, to make the self-cleaning process easier and reduce any embarrassment of having to ask an attendant for one (though trust me, they won’t bat an eyelid, they’ve see so much worse…)

• You could even bring a flannel/sponge/washcloth and a small travel/gym towel plus some airtight bag like a ziplock or dry bag to seal them in once wet. For the true “luxury” commando shower, this Flyer Talk thread chx linked to includes the idea of putting some of your favorite shower gel on your washcloth, before putting your shower gel bottle in checked luggage, then sealing the soaped washcloth in a ziplock bag and bringing it to the plane ready to wet and use.
• Some stores sell “anti-odor” or “anti-microbial” clothing, which could be an option for a frequently-stinky frequent traveller – but it might just be expensive quackery

As you say, the best way to avoid being that guy is to try and wash yourself in between flights. When showers are not available, you can use (scented or unscented) baby wipes to clean your armpits and other exposed smelly body parts. You can wash your face and neck in any restroom sink. And don’t forget to brush your teeth. Changing shirt/t-shirt is also very helpful.

Here’s what I usually do during long haul flights. I carry mouthwash and a toothbrush and use them when I’m in transit. I then usually go to the duty free stores and try some perfumes 🙂 It also helps if you carry an extra tshirt. Alternatively if you have some of those small roll on deo’s, those will help as well