Transistor count of floating point multiplier
I'm writing this with no experience what so ever, so take this answer with a grain of salt. That said...

A typical 32-bit float has 23 bits of fraction. Multiplying two of these only requires a 23x23 multiplier, keeping the upper 23 bits. The exponents are then added. Adds are cheap.

Your 32-bit integer has 32 bits, so you need a 32x32 bit multiplier, keeping the upper or lower 32 bits.

So: Your floating point multiplier ought to be cheaper.