cough relief

That's the normal way editing in GB works (since it's originally a music tool and automatic truncating would throw everything out of the groove). Just cut before and after the cough and delete the little region in the middle. Make sure you cut at a zero point of the audio waveform, otherwise you'll hear a click!

If you cut and delete, you create a gap, yes - and that's why the vocal track stays in sync! A gap is nothing but silence.
(If you want to avoid a gap, there's a separate menu command "cut and move" - but that's exactly what you don't want!)

If you want to make it more obvious that it is just a gap, then use the volume curve to silence that bit of the track.

You could also use a technique often employed for 'live' tracks in the film industry: if there's a space anywhere on the vocal track where nothing is happening, you can make a looped track of that 'room tone' and then cross-fade it in and out any time there's unwanted noise between vocal parts.