It should only take an hour or so. I wouldn't advise playing anything on your new system at all. You can't selectively choose what you transfer or not. It all gets transferred, and your target system gets wiped first, and then after that your original system gets wiped. And if you set up a Nintendo Network ID on the target system, that can complicate things.
Or maybe what you're saying is, what if you deleted everything on your current DS so that it wouldn't try to transfer it all via wi-fi. That could work! There are methods to transfer via PC, too, but frankly I can't seem to access my New 3DS via PC at all. If you have a microSD to SD adapter, though, and a PC that reads SDs, you could do that...
I think you said before you have less than 4GB of stuff, right? I think if I were you, I might just back up my save data I wanted to keep (using the on-board thing on the 3DS where you click the little arrow), delete everything, then system transfer. Then re-download Monster Hunter on the new one after the transfer and go at it.
Or, if you don't want to fiddle, just do a system transfer normally and let it take its time. I suppose what takes the longest is beaming data from one 3DS to another over wi-fi. With mine, it was all on a microSD in an adapter and I just popped it from the old to the new without adapter. And it still took an hour. Why? I don't see why transferring licenses or whatever it's doing should take so long...
Edit: I see now I totally misinterpreted what you were saying/asking... sorry.