Normally you would clip the counters' points with a nail cutter or something.
Correct. Old grognards clip the corners of counters with a nail clipper. This is done because on a regular hex map, with stacks of counters sitting adjacent to each other, the corners of the counters protrude over the lines and tend to create disorder; especially when moved or when they fall over, or when you have to dig for the one on the bottom.
Other old time wargaming tools include a good set of tweezers and sugeon steady hands for picking out stacks of counters from the close together piles, and for picking off counters one at a time when digging through stacks. Also useful for "dressing the ranks" (straightening stacks of counters) and pushing stacks around (when not too close to other stacks).