Your only concern is about engine failure after take off, the probability of that is very less.
When flying at Vx, and any delay in recognising the engine failure will result in stalling of aircraft and the situation becomes venal.
If u climb at Vy, the chances of making a safe landing after turning back to the runway are higher than Vx(in this case the aircraft will tend to overshoot).
Last week I came across an engine failure of a SE aircraft turning crosswind, at my aerodrome. The pilot turned to the field and landed in the opposite direction, he was able to stop just at the end of the sealed runway. He was too high and had to do sideslip in order to get down. The normal procedure for that aircraft states to climb at Vy. IF they had climbed at Vx, surely they would have overshot.