Put it this way, maybe it's OCD but I, personally, won't work in dirty kitchens - places where there are dirty dishes left piled up in the sink when I am supposed to be replacing the worktop, or where food waste hasn't been cleane away, and that sort of thing. Not opposed to dealing with muck and rubble on site, but really - in someone's kitchen? [/Rant-off]
Silicone should always be laid on a fresh, clean surface. Yes, it can be a bloody awful job to get the old stuff off, but if you want to do a professional looking job which lasts you need to do this before applying new silicone
Don't apply too much silicone - it is better to apply too little on the first run and "top it up" with a tiny extra bead before wiping across with the silicone finger - this must be done promptly, not an hour after the first application. Do not apply great gobs of the stuff (and that means don't cut too much of the nozzle off, too!) and hope you can wipe it off - you can't, as you've discovered. Clean your silicone finger regularly, and thoroughly, and never let the silicone build up too much on the silicone finger. To control your application better, buy a better quality caulking gun, something like a Cox heavy duty, Ox heavy duty or my own favourite a Tajima Convoy - apart from better control, and longer life, these heavy duty guns have one really big advantage - if you cut off the flow by taking the pressure off the flow stops almost immediately, something skeleton guns aren't good at