Yeah debit works the same as credit cards for these things (notice the eshop only says "credit card"). The only difference is that you're spending money you have, not money you have been credited.
You could always buy a regular flashcart and use the new TWLoader that runs the 3ds like a dsi and lets you use older flashcarts that aren't suppose to work in the 3ds. (TWLoader should let you load roms directly from sd card in future)
So if you've already got an r4 that isn't compatible with 3ds, I'd give that a try first before buying a new one.