How Math Heavy is Graduate Finance
Programs vary; it would be best to look at the specific requirements and prerequisites for the programs you have in mind.

In general, mathematical finance can involve a very considerable amount of pure mathematics.  A big piece is modeling assets via stochastic processes, and to understand those properly requires a firm background in graduate-level real analysis, measure theory, probability theory, and often functional analysis and PDE.  A mathematical finance course may well consist primarily of theorems and proofs, just like a pure math course would.  This is typically even more true at the PhD level than masters.

Of course, I would say that just because mathematics is challenging, that doesn't mean you should avoid it!