Correct company-issued remote intended for the M10S:
p/n RM-SDR009J
Correct company-issued remote intended for the MV-1S:
p/n RM-SDR013J
see differing photos below.
I have a few each of these JVC decks, too, but I use whichever model remote was assigned to the specific model...Less chance of wearing its keys, its batteries or a single unit itself down. Six of one, half a dozen of the other; It's up to you- whichever you prefer, I guess?
Hope this help you!