new wheels would be reassuring for sure.
however, a reputable/experienced repairer should be able to inspect and determine if it's fixable AND be safe. though they may not know for sure until they attempt to 'roll' it back into shape, then inspect and i think they can xray them if required.
my wife had a buckled wheel repaired on her Subaru, and they assured us it's fine.
minor issue is that part of the process involves heating the wheel, and this discolours it. so if the affected area is on the 'front', you may want to have it resprayed.
overall, it should still be far cheaper than 2 new wheels. my wife's repair was AUS$150ish, without respraying, and a new 16" Subie wheel is AUS$800+.