Pretending pure math is applied math for grant funding
This won't be a direct answer to your query, but I hope will be useful advice. First, if you must do pure math and you must get funding to do it, then you have no option but to apply. If you don't apply, you don't get funded. 

Next, being devious isn't going to help you and will likely be recognized, as you fear. 

However, on some time scale, all mathematics is applied. The time scale may be long, of course. In my personal case, it took about thirty years for someone to find an application for my "beautiful" but extremely arcane dissertation to find application. I'd predicted that it would never be done. But thirty years isn't very long, so that doesn't help you directly. 

You work in some subfield of mathematics, of course. It might be very narrow and it might be a currently popular subfield, or not. But it is likely that others in the same subfield, or a closely related one, have seen applications of their work to some problems. If you can learn what those applications have been, you have the basis for a statement that "Advanced work in X has been known to contribute to Y as evidenced by (citation)". That isn't devious, or phony. 

But note that "applied" is actually a continuum, not a discrete thing. Pure is pretty far to one end of the continuum, but it isn't disconnected from the other. But it will take some investigation on your part, and I suspect that you are good at that sort of thing.