I'm running my guitar through a crappy 60 watt behringer head attached to a 4x10 bass cab.

Would it be okay to simple buy a new, better head or would the cab give me problems with the higher louder guitar frequencies?
Dude keep the cab, i use one and they sound sweet. A lot of guitar amps use 4x10 speakers

Proco Turbo RAT
Boss RE-20

Fender Blues Junior