Throughout the pandemic, I've been sending stuff from Aus to the USA (I have a classic car and buy/sell parts through a hobby forum), and this stuff is heavy.
I never use FedEx or UPS since they're always way more expensive. USPS International seems to be priced about the same as our Australia Post Standard International (by air) and usually takes about 14 days door-to-door either direction. Can't say I've sent anything to the UK lately, I think it should be fine if you choose an option that has tracking included, as that will let the recipient follow the journey too.
I think the warnings about delayed timeframes is about standard for the postal/shipping industry nowadays, just gives them some wiggle room over the pre-covid standard delivery times since there are fewer worldwide flights.
Probably a good idea to talk to your local USPS office about options, and also any insurance that you or the buyer may require, and then check with the recipient that they're comfortable accepting the terms - noting most 'economy' (rather than 'standard') methods are cheap but usually slower and less reliable than a message-in-a-bottle