Transpose/key change on midi sysex command

Transposition is a live-patching action on MIDI stream that, IMHO, must be done at the player side (by your karaoke player), not at the device/render side (VMS).

I don't know why your player chose to send a custom SysEx instead of "patching" the MIDI stream.
Maybe because it's bundled with dedicated hardware... but I still think it's not a good choice.

Have you double-checked that's the only transpose-option it has?
VanBasco MIDI player, to name one of the lightest and performant karaoke players (even if now aged), does transposition as like as tempo change "in house", by raising/lowering all notes (except for the drum channel) before sending'em out to the MIDI device.
This way it's automagically compatible with each MIDI device, real or virtual.

Till now VMS is "transparent" about the MIDI stream, with only an "exception": volume/mute/solo.
To be honest it also can limit reverb/chorus effect; this feature was added "under pressant demand" of some users 😉; at that time I thought it was a good idea... but I was badly wrong!
I should never have added it, since it lead to a lot of bug reports from other users that didn't want it (lot of threads in the forum) or wanted it to behave differently. And it also interfere with reverb/chorus management done by featured players.

I was also asked to add features like "change programs" (instruments) on the fly, but I've declined them too.
I still think VMS is a (virtual) device, not a player; and patching must be done at player side.

That said, the MIDI rendering in VMS is done by BASS libraries (as like as the SysEx management).
You could try to ask them if they'd like to support those SysEx messages...