Nearly two years later and this problem still hasn't been fixed.
One way to "solve" the retching noises from continuing to play, according to a forum post on Steam, is to disable the sound effects in the game, then switch them back on after a few minutes. Not exactly ideal, but THQ Nordic doesn't seem to be interested in fixing this issue.
Hey everybody! I just discovered that somebody over on the Steam forums was able to provide a fix, it's done by replacing two files in the sound directory with patched versions.
I tried on the GOG version and it didn't work, but thankfully, the patch package included instructions on how to patch the files in question yourself, and I did that and now the bug is really fixed. Blob does the retching noises when inked, and they stop after washing the ink off.
You can download the fix here, it includes my versions of the patched files for GOG. Just check out the README inside for instructions. https://drive.google.com/file/d/1jw7R7DeDfvtGSokBicGvmHZhkrSFPQrO/view?usp=sharing