Conversion to horizontal dropouts (for fixed gear), V-brake
V-brake calipers have a radial (with respect to the wheel) adjustment range, so they can accommodate the wheel axle moving fore or aft a little.
What you need to do is make sure that the placement of the new dropouts does not place the wheel axle such that the brake track on the rim is outside the range of caliper adjustment.
You could do this with a simple cardboard template that marks the axle to brake track distance.