That should work. Just to be self-assured, knock out all but one stud, place the desired replacement wheel onto the axle using the remaining stud to center the wheel and mark the to-be-drilled holes. This will show any problems that you may have to weld up and dress down prior to drilling. The two holes closest to the 9 o'clock and 3 o'clock positions are the most likely to have a proximity problem. If you keep the axles cool with wet rags while you are welding, if welding is necessary, and if you are not going to expose to all-out racing conditions afterward (although I have done so for circle track racing), you will not compromise the temper or straightness of the axles. When you drill the new holes, be sure to leave enough metal in them so that when you install the knurled portion of the stud, you have to press or hammer them in to seat them.
As stated, you probably won't have a problem.