Upvote:1
Use your UK passport.
UK/USA "special relationship" means that UK is part of the Visa Waiver Program. Select countries thus don't need visas,since the USA deems them less risky.
Guyana would require a visa for entry.
When applying, you would have to state you have dual nationality, but then this shouldn't be an issue for the US border control. You should ensure though you do enter with your UK passport, possibly even show your Guyanese passport on entry too.
Upvote:6
Easy, just use both passports, as explained in detail here:
The main catch is that, if country 1 really cares about you not having multiple citizenships (can you tell us which country it is?), immigration officers may look for visas for/stamps from the US and start asking awkward questions if they can't find any. The usual ploy around this is to swap passports at a connection point: for example, dual Malaysian/Australian citizens usually travel via Singapore, so Malaysia thinks they're visiting Singapore only (no visa needed).