Every country is different. In the UK you would probably need an Direct Airside Transit Visa (https://www.gov.uk/transit-visa), in the US you may need a C1 Transit Visa. https://travel.state.gov/content/travel/en/us-visas/other-visa-categories/transit.html
It does not only depend on the countries you go through but also on the exact way your flights are booked (single tickets, multiple tickets, layover lengths, etc.)
Trying to get to Georgetown, it's hard to avoid the US or Canada. You could try routing through the Bahamas or Cuba and see if that's easier.
This may be one of the few occasions where a knowledgeable and experienced travel agent would be helpful.