Yes, it should be fine. I have the native wild version, Euonymous atropurpurea, the so-called "Wahoo Tree", and I wouldn't be afraid to prune it now. I actually cut mine down to stubs every 8-10 years, otherwise it gets full of old, dead and weak growth and seems to lose vigor.

Have been pruning my BB back to 3-4 ft every spring before bud break for 10 yrs, no problems, must occasionally remove a couple of entire branches to keep vigorous.