first, "Walkman" is a trademark pocket-sized stereo system so, remember that it should be written with capital letter. I found "Walkmans" in Oxford dictionary that defines it as simply the plural form of "Walkman" :)

Good question. I'll go on a tangent to answer it. At the beginning of Lord of the Rings (no seriously, read on), Bilbo thanks many hobbit families for coming to his 110th birthday. He mentions the Proudfoot family, and calls them the "Proudfoots". He's immediately corrected when a Proudfoot yells out "ProudFEET!!" So my answer is... it's your choice! We native speakers will understand both. Run for a dictionary? Remember it took us English speakers over a thousand years to come up with one... :P

Ummm, Google tells me people rarely will say 'Walkmans' (despite few search results) and though 'Walkmen' is actually a band. So, it's embarrassing - in any way '---mans' will sound odd to people but damn it Walkman is just a made-up word, so... I think 'Walkmans' is OK. No important.

Walkmans. A walkman isn't a man who is walking so we treat it as a regular noun and add an s (instead of treating it as a kind of "man" and use the plural form of man, i.e. men) to pluralize it. in morphology we call it an exocentric compound (exocentric compounds are "compounded words in which none of the members can identify the general class to which the entire compounds belong"), just like "saber tooths" - we don't say saber teeth because they aren't a kind of teeth but animals. (we do say policemen instead of policemans because a policeman is indeed a man)