Could the fact that you are playing a weaker opponent tomorrow at the Varsity level equal playing time for you at the Varsity level? Maybe he'll give the starting catcher a day off or at least part of the day off to a)give him time to rest and b)get you some Varsity experience.
As you know, catching is extremely difficult on the body. Blocking balls, squatting down a lot, etc. Playing a "weaker" opponent would be a good opportunity for the coach to get some of his starters at least a little bit of a break.
Unless there is not another catcher able to step in at the Varsity game, no I would not think you would want to ask to go down. JV coach asking for you, Varsity coach asking you to go down-yes. You asking--probably not a good idea.