Congratulations!
On the one hand, I see your point–I think a lot of people I know would look at Artyom and just go, “Uhhh… [name_m]Artie[/name_m]… I’m sorry, I’m just going to butcher that.” ([name_m]Even[/name_m] with the healthy number of Russian and Slavic people in the area. There’s not a ton, but I know a rather large Belarusian family, and they seem to always have Russian-speaking friends tagging along! I think some might be north a state or so, though.) On the other hand, it seems like Artyom is pronounced just like it looks.
If you don’t want to go for Artyom, and want to stick to an “A” name, I don’t think you need to swing to the opposite end of the spectrum and go with a trendy (and, in the opinion of some, overused and tired) name like [name_m]Austin[/name_m] or [name_u]Aidan[/name_u] that your wife probably struggles to relate to culturally. Personally, I’m an American mutt, but if I married into a family with strong ties to another nationality, I would TOTALLY embrace that for our children’s names, although that is probably because I have a huge thing for names from other cultures! Have you looked at other Russian “A” alternatives? So far I’ve come across [name_m]Abram[/name_m] (which is said differently than in English, but still very cool, and not too hard to enforce. It’s also very hip/stylish right now, and the nns [name_m]Abe[/name_m] and [name_m]Bram[/name_m] are very vogue, as well!), [name_m]Alexander[/name_m] (timeless!), [name_m]Alexei[/name_m] (le swoon!), [name_m]Anatoly[/name_m], [name_m]Andrei[/name_m] (I know a Romanian [name_m]Andrei[/name_m], and he seemed to do just fine with it!), [name_m]Artur[/name_m] (and [name_m]Artie[/name_m]/[name_m]Art[/name_m] would work here, as well), [name_m]Anton[/name_m], [name_m]Arkady[/name_m], Avgustin, [name_m]Avel[/name_m] (which I assume is the Russian form of [name_m]Abel[/name_m], which is super hot right now, but I am not 100% sure), etc. It seems like quite a lot of those would bridge the gap well between her Russian culture and maybe something a little bit easier for your family (and English-speaking friends/acquaintances) to pronounce/accept.
For what it’s worth, I see no problem in introducing oneself as [name_m]Art[/name_m]. “[name_m]Hi[/name_m], I’m [name_m]Art[/name_m].” Why not? I know an [name_m]Arthur[/name_m] who probably does the same thing, and I don’t think most people would freak out about just [name_m]Art[/name_m]? They may ask, “Oh, is that short for anything?” but most people seem to do that when people introduce themselves by a nn.
Good luck!