if they are different enough, then you shouldn't have too much trouble. I've been learning Japanese and German at the same time and it hasn't given me any trouble.
The most important thing is that they sound different, I think. Even though I already basically knew Spanish completely by the time I started studying Japanese, I still sometimes mix up words that have about the same meaning and could occur in either language phonologically, e.g. I sometimes mix up "pero" and "demo" (but never aber.
imo, Latin and Japanese are probably different enough that you can learn them both without too much difficulty. You probably wouldn't ever have trouble with morphology or syntax because the two use completely different morphological strategies; if you have any problem with vocabulary it would probably with indeclinable words like "tamen"