Would I be able to safely run a bass through my guitar crybaby 535q? I know it may not sound ideal, but will I break anything if I do?
It won't hurt anything. I don't know if that particular model was designed for bass, but I do know the orignal Dunlop Crybaby was made for the bass guitar.

There shouldnt be a problem, depending on the amp that your running it through you MIGHT lose some low end.
Treble>Epiphone Prophecy EX - MXR micro Amp - MXR Blue Box - MXR Fullbore - MXR Noise Clamp - Vox AD30VT
Bass>Ibanez BTB505 - MXR Blowtorch - MXR D.I. - Peavey MaxBass 700 - Peavey TVX410
Short Answer, no. Long answer - no but u might lose that nice sound w/o a bass specific model.
I love Prog, +1 for synth solos and songs about maggie thatcher.


Geddy Lee Jazz (Black )
Fender Rumble 100 (It lights up )
MXR Auto-Wah (Purple... )
Boss Bass Overdrive (I can almsot sound like Chris Wolstenholme )
It will work, it just won't sound good. The bass Crybaby is basically the same as the guitar model, there are just a few components different, to 'tune' the wah to the frequency range of a bass.
With a guitar wah, the sweep won't really affect lower notes, because it was designed for use with a guitar.