Can I choose different value capacitor?
I'd say the 0.047uF capacitor would be fine but do check it's X or Y rated for use on the AC power - just because it says it is 250VAC it doesn't mean it won't fail disgracefully and burn a hole in something (or worse).

I would also ask you to double check the value of the capacitor you are removing. I'd have guessed your sewing machine motor to be rated at maybe 100 watts and a cap I replaced recently on a 350 watt motor was 6uF. However, this was for an AC induction motor and something in the back of my mind makes me think that sewing machines use DC motors - if you can control the speed with a foot switch then it is a DC motor and the incoming AC is rectified - speed control could be via a thyristor/triac/SCR circuit OR via an extra field winding on the motor.

However, if it is an AC motor then the reason why the 0.15uF capacitor would probably be no good is that on many types of single phase induction motors there are two windings and, rotationally, they are spaced 90 degrees to each other. The winding fed from the cap has an inductance that together with the capacitor form a series tuned circuit at 50 Hz or 60 Hz or whatever AC frequency you operate at. A series resonant tuned circuit produces a voltage phase angle across the coil that lags the other coil by 90 degrees thus matching the mechanical position. This means that the rotor rotates one full rev in 20 ms (50 Hz) or runs at 3000 rpm.