why is it mentioned in the pali canon that Without the direct guidance of a teacher, this practice can be dangerous,

I am not sure if this is mentioned as dangerous in the canon. It is in the commentaries which say this is dangerous. It can be inferred as dangerous because of the above incident.

does this mean that I being a layperson, can't perform this?

You can do this. Only if done right it is not dangerous.

moreover, how can I not develop aversion while practising this but still reap it's benefit?

This is recommended if you inclined to see beauty in the physical form. That is, when you see something you evaluate it is beautiful you get strong attachment.

What is involved here is perception of beauty and the sensation.

Develope Opposite Perception and View

When you see a certain form or shape as beautiful then develop the perception and view that is is not. This way, as your practice mature, your mental reaction to something beautiful will lesen. The form can you your form (own beauty or looks), someone else or even imaginary form.

when a monk sees a form with the eye, (in him) the agreeable arises, the disagreeable arises, the agreeable-and-disagreeable [the neutral] arises.

...

If he wishes thus, ‘May I dwell perceiving the repulsive in the unrepulsive,’ he dwells perceiving the repulsive therein

... mind-object .. mind ...

Indriya Bhāvanā Sutta, Sampasadanīya Sutta

Cemetery Contemplation

Also use external form to reduce attachment to ones own body, again at the level of correcting the perception and view as well as the reflexive response of the mind, i.e., to reduce reflexing arising of craving for sensation due to perceptions on form, and should not lead to reflexing arising of aversion for sensation due to perceptions on form.

he compares this very body with that, thinking: "Such is the nature of this body: it will become like that—this is unavoidable."

Mahā Sati’patthāna Sutta

Changes Perception and View due to Internal Content

Also think if what is within the body is external and what was external was inside, you will be chasing animals away from pecking at you flesh! Also imagine what is below the skin. What comes out of the orifices. Imagine body parts piled up. This also a change in perception and view. The last view to break is that the stream of consciousness in internal or self.

Also see: In what Sutta(s) is there a References to Imagine the Body Inside Out and What is Below the Skin, Sampasadanīya Sutta

Whole vs. Parts and Effect on Perceptions and View

The body is made of parts. Sum of the parts are beautiful but not individually. The parts on their own does not have beauty, but put together only the perception and view of beauty arise. This way you reduce the mental reaction and attachment, to the sensation due to the mental reaction, that follows.

Also see: Mahā Sati’patthāna Sutta

Change in Form due To Decay Changes Perception and Views

Developing the view that the body is impermanent, subjected sickness, decay, old age and death. When you see someone beautiful then when they are sick, oozing excretions or on a pile of excretions, old and dead. Again this a way to adjust your perception and view so you mental reaction and the craving that result from the sensations due to how you mind's reactions are diminished.

Also see: Maha Dukkha-k,khandha Sutta, Does any Theravada Suttas / sources refer to Oozing orifices? What are the Suttas?

Method on Insight

Also when you evaluate some form as beautiful, plain or ugly you get a pleasant, neutral and unpleasant sensation. Use this to eradicate you latent tendencies for craving.

On seeing a form with the eye,

one explores a form that gives rise to pleasure,

one explores a form that gives rise to pain [displeasure],

one explores a form that gives rise to equanimity.

...

On cognizing a mind-object with the mind,

one explores a mind-object that gives rise to pleasure,

one explores a mind-object that gives rise to pain [displeasure],

one explores a mind-object that gives rise to equanimity

Sal-āyatana Vibhanga Sutta

the latent tendency to lust reinforced by being attached to pleasant feelings;

Pahāna Sutta

In the methods mentioned above, the 1st can be dangerous (from most dangerous to the lesser dangerous ones), if you develop aversion towards form, due to the pratice. This is what happened to the monks who committed suicide. They got repulsed by their own body. Meditation on repulsiveness is to bring balance to your mind (being equanimous know it is impermanent regardless of the mental reaction) than moving from one polarity to another (i.e., reflexively seeing beauty and develop craving to reflexively seeing repulsiveness and developing aversion). Developing Insight is the safest way to practice this form of meditation as you are not trying to adjust you reactive / reflexive response of the mind with the risk of overdoing it. A experienced teacher may help detect if you have overdone it and reduce the risk.

Also see: Patikulamanasikara, Vipallasa Sutta