You must trim any silicone as thin as possible, using a sharp knife first. I then wipe with IPA/meths for ensure 100% dry. Then apply remover and go for a couple of cups of tea.
When you come back just use a non metal scraper, nylon pot scrubber etc to remove the now loose silicone "film".
Wash with water. Water deactivates the remover.
Dry, clean with IPA/meths, apply masking tape, apply silicone, smooth away with your favourite tool and/or finger soaked in Fairy liquid solution. Job done.
Soudal (at some B&Q's) also sell a silicone remover which I have used a couple of times. Similar results to Screw fix stuff.