I plan to connect balanced TRS output with unbalanced TS input and I wonder if instead of cutting the cable and leaving ring floating I could just cover the male jack itself (the ring part that goes to the unbalanced input) with insulation tape. My guess is it should prevent the signal from the ring connect with the sleeve of the unbalanced, TS input.
Both are terrible "solution" in that they are no solutions at all.
Conversion from balanced to unbalanced isn't done by isolating conductors, since the "other" side of the balanced signal isn't at a defined potential. That's the whole point of balanced signalling. The potential difference between the two balanced conductors is driven by an output driver, but if you make one float and connect the other, then chances are that he floating one is the one that will be driven, whereas the one that you connect will be more or less at a fixed potential relative to the receiver. "More or less", because capacitive effects will probably make this sound like a high-pass signal.
Instead, properly convert your balanced output to an unbalanced one: A signal transformer would do that.
In a pinch, connecting one of the balanced lines to ground and using the other would probably work, too, but only if the introduced offset is in the range of what the output can drive.
Instead of cutting anything or sticking tape on things, just build yourself a short adapter cable from an inline TRS jack and a TS plug. Then, you can explicitly either wire the R to S or leave it open, as appropriate for your specific signal source. You could even include a small SPST switch that allows you to select either option.
In an ideal world, you'll make sure that both T and R are terminated with equal impedances to S — in which case, the switch becomes unnecessary.