Just wanted to share one of my personal essential tools for repotting smaller cacti. Pardon the watermark... this is not my photo.
I find this style of tongs incredibly useful when repotting smaller cacti, especially those with longer spines that can be tricky to work with through other means. The shape of the tongs easily gets close to the plant body without damaging the spines. Once the plant is loosened, I'll use them to carefully lift them out of their old pots, as well as to hold the plant steady while filling around it in the new pot.