I really don't think it is as simple as some seem to think. Effective communication is not about saying what you 'mean', it is about the person you are talking to 'understanding' what you said as meaning what you meant to communicate. Jimlad48 has given a very clear example of how that can go horribly wrong sometimes. It can also happen even with relatively simple things like confusing what the words 'first floor' mean. In N. America it of course refers to the 'ground floor' which is the 'first' floor in a building. In the UK it refers to the 'first' floor above the 'ground floor' which in N. America would be called the 'second' floor since it is the 'second' floor in a building. There are many such differences that can indeed cause a 'failure to communicate'.
Rather than focusing on words that most people in both countries understand as being synonymous, it is the words that are spelled and pronounced the same but have entirely different meanings in the two countries that you should be concerned with getting right.
The UK is a 'foreign' country to someone from N. America and should be treated the same as Italy or France or wherever. You strive to be understood in whatever way you can, using whatever knowledge you have. In other words, 'when in Rome, do as the Romans do.' Do not do as you do at home and expect the other person to figure out what you were trying to communicate to them.
I try when travelling to other 'English speaking' countries, to speak in as simple but specific English as possible as this is most likely to cause the least misunderstandings. I always remember asking a young (early teens) waitress in a hotel in Scotland for 'brown toast'. In Canada we generally say 'brown' toast while in the USA, 'wheat' toast is more common. When I asked for 'brown toast' meaning whole wheat bread toasted, the young waitress in Scotland looked at me like I was an idiot and replied in all seriousness, 'all toast is brown.' She was of course correct and I had failed to communicate clearly to her what it was I wanted her to understand what I said meant.
Colloquialisms are the most common area of language where this can occur, like the toast example but the problem is we often don't know that the word we use every day is in fact a colloquialism. Again, Jimlad48's example is a case of a colloquialism and in that example, a colloquialism in both American English and British English which has an entirely different meaning in both. Whichever meaning you wished to convey could be made clear by using the more formal or literary words rather than a word that may be misunderstood. You cannot mistake what I want if I ask for 'whole wheat bread, toasted.'
Here is a list of common word differences that can help.
https://www.adducation.info/lifestyl...merican-words/
Take another simple example like 'chips' vs. 'crisps'. Asking for some 'chips' with a sandwich will get a N. American 'french fries'. Knowing to ask for 'crisps' will get them what they actually meant the person they asked, to understand them as wanting.
Some can be very amusing. I like garter belt vs. suspenders. If someone from N. America says, 'he wears suspenders' the reaction from a Brit could be quite laughable. Or how about, 'knock you up'. The first time a Brit said that to me (I'm a guy which made it even more confusing), I didn't know what to think. There is a big difference between 'get you pregnant' (N. American) and 'knock at your door' (UK meaning). LOL
So, I would say overall that there is absolutely nothing wrong with trying to get it right in terms that a local will understand and there is certainly nothing 'pretentious' in trying to do so. Just know, you will probably get some wrong and hopefully that will be cause for both parties to have a laugh together.