Thanks for further varieties! I hadn't seen the ring, and have had such a clicker but have not got the hang of using it non-awkwardly (where do you put it? With your keys? Who knows where those are? In your pocket? Who reliably has a pocket that fits things in? In your bag? Then you have to dig it out..)

Good point regarding wanting to know what number you have reached. I only want to know the exact number very occasionally, like with a bank account, but I agree that's not true of many use cases.

I grab the string and/or some beads I don't want to move together between my thumb and finger on one hand, and push the bead I do want to move with my thumb and finger of the other hand. (I don't need to see it because I can feel it and the beads don't move with my touching it.) I can also do it more awkwardly with one hand.

The static friction is high enough that the beads will only move if you push them, but low enough that they are easy to push. The necklace is made of 2 strands, joined at the endpoints. Put one strand on the table in the shape of $y=\sin x$, the other goes on top of it in the shape of $y=-\sin x$. The beads go around the crossing points of the 2 strands, as rings in the $x,z$ plane. (You don't have to make an exact sine wave of course, anything that yields the same topological result will work, and to loop the beads around the crossings the way I've described, you''l have to thread the strands through the beads before joining them at the end.) Having the crossings pass through the beads increases the friction, since the bead is redirecting some of the tension in the strands.

In theory, putting beads in the normal way on a single strand could also work, if the diameter of the strand and the hole size of the bead were well matched. (You'd want fray-proof string for threading that not to be a huge pain, though.)