There are two forms of the conditional in everyday use across Wales, so it depends on where people come from. This thread contains quite a lot of information - Byddwn and baswn
though fyswm ni is not a variation I’ve heard before. The ‘m’ ending for the ‘we’ forms tends to be more literary than everyday Welsh - perhaps they’re saying fyswn ni which can be a north Walian variation of baswn ni
But whichever form they’re using, if that’s the way your local first language Welsh speakers say it, go with them 