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Whether you can get away with self-studying and the admissions believing you is outside my knowledge, so I'll leave that for someone else to comment on.
Looking at a few of the top 10 MFEs according to QuantNet namely CMU, Baruch, Stanford, and Berkeley, here is a sample of their prereq math courses:
PDE
Probability
Calculus (DE, multivariate, etc)
Linear algebra
Numerical analysis
Some programs also ask for familiarity to fluency in a programming language such as C++ and a statistics package (Matlab, R, Eviews, etc)
Here is a nice quote for you from the Stanford Financial Mathematics FAQ:The single most common reason applicants are rejected is their math background is not strong enough.