its a good idea.
When I see tape on test leads I want to hurt people. It means they don't care about your test potentially getting messed up when the tape falls off and you do a accidental swaparoo.. don't do this. Bad habit that means your desperate.
Heatshrink is acceptable, but it can slide off. Adhesive lined heat shrink is better and is cleanable.
A good quality paint job is also an option, but painting plastic durable is kinda hard since its on plastic. You would need to experiment with paints to see what gives a durable layer.
Those color bands also like to slide/pop off. I recommend putting clear heat shrink on them, over the indicator ring, if you can (you need a high shrink ratio to get it over the probe sometimes). And a sharp tip scissor to get them off to slide under the heat shrink when you need to change it, so you don't damage the probe trying to cut it off with a knife.
Since the colored cap slides off easily, you would also need to color the probe with the ring. If you have color rings and also tips that match, that is great.
And you want to label the probe anyway, because you might be using the spring low inductance ground lead sometimes.
Take measurements to determine what shrink ratio you need, if you want to do this, and search on digikey for the correct heatshrink.
Always amazing when you have such a expenisve scope, expensive probes, then you put electrical tape on it that ends up having a little skin tag, goos it up like a slobbering xenomorph and then falls off
Colors are worth investing in ! And you cut small heat shrink bands and use the thinner material so its not annoying... but you can't guarantee that the heat shrink might not annoy your fingers if you work with it alot, then paint is your only option.