I now want to transfer the music to an MP3 type player. Ideally I'd like to transfer the WMA files as they are (e.g. not reconvert to MP3).
That wouldnt be advised anyway as most people tend to only use shoddy bit rates so converting will produce an enormous change in the quality as does all transcoding. WMA support tends to vary. My player doesnt like WMA at all but then WMA only beats mp3 for quality at bitrates of 64kbps or lower so I would tend to use mp3 as overall it is better supported, doesnt limit your player choices as WMA does. MP3 is ubiquitous to all but a few players.
There is no way we can tell you if VBR WMA will be supported however I would seriously consider in your situation converting to mp3 as WMA even when supported can be poor as I know on my player some WMA plays others it cannot work with. Of course it is your choice but in doing so it seriously limits your choices. I have had to do this myself as I liked ogg more (another format) but the player doesnt support it so had to convert my 6000 song library to mp3.