Compact binoculars 8x20(21) or 10x20(21) would be much easier to use and not bigger than monocular. Often can be found on sale for your target price. I have a pair of BSA Compact 8x21 and Bushnell that I use all the time to scope hits up to 100m on the metallic silhouettes. Paper holes (22cal) can be seen up to 25-30m, larger 9mm or 45 holes seen to 50-60m.
I also have a more expensive Vortex Solo monocular 10x25 (~$50) that is not any better, nor more compact, but harder to use.