Sq taper BB are readily available, I agree with alcphil, your axle is unlikely to break, its most susceptible part to breakage is the axle-crank retention bolt if
you overtighten it.
http://www.bikeforums.net/road-cycli...-injuries.html
http://www.bikeforums.net/road-cycli...kes-again.html
http://www.pardo.net/bike/pic/fail-001/FAIL-202.html
I can't trust the bottom bracket. I've already suffered a crash (fortunately not from component failure) but I have had a component fail before That time I was not wearing a helmet and had things turned out differently I could easily have ended up under the wheels of a bus. I'd rather dance on the side of caution this time.
Also even if the cheap BB doesn't fail it will almost inevitably end up useless within a few months of use. I've had a similar cheap square taper BB on an old bike and the BB developed tons of play within two months of riding. You could easily swing the crank arms side to side. The bearings were shot. I had the bearings replaced and the entire thing tightened up but it was still a bit loose. Might as well bite the bullet now and switch to a reliable, durable bottom bracket.