I have tried to paint RTV (Room Temperature Volcanising) silicone onto wood (the silicone that soap liners are made out of) but this does not work very well because 1. RTV is not thick enough to make a consistently thick layer 2. It is selfreleasing from EVERYTHING, so it will peal off the wood easily.
The silicone from the hardware store that comes in tubes is a silicone 'adhesive' (VERY different from RTV silicone) that can stick to bathroom and other surfaces like wood moulds, but I would use a lot of caution with 'silicone' from the hardware store because there are a lot of "nasties" added to the tube silicone to make it adhesive - some even say to avoid contact with your skin, so you never know what might be leaching out of the adhesive type silicone into the soap. It's just a possibility, because hardware store silicone wasn't meant to be used to line moulds that will contain skin care products, so you never know what they would add that wouldn't be compatible.
I also wanted to suggest that you use shellac for your wooden moulds. Shellac is a natural resin (it's even used to coat skittles!) that is very safe and easy to work with, and a shiny plastic like surface can be build up with some patience and lots of layering. Even with just a few coats and some fine sand paper you can get a very smooth sealed surface.
Soap sticks to wood because wood is porous and rough, so the wood needs to be smooth and sealed to assist with non-sticking. (although wood is not flexible so there may need to be some oil or food silicone spray to between the soap and smoothed wood to lubricate and assist it's removal).
To seal and smooth your wood with shellc:
1. You'll need: Shellac flakes (these are the elytra for lac beetles!), methylated spirits (or ethanol), sponge wrapped in lint free cloth about the size of a small golf/base ball, and two small leak free containers.
2. Mix the shellac to the recommended consistency as on the back of your package, I usually make my mix a bit thinner than the back says. When dissolved in a few hours give it a good stir,
3. Sand your wood with a light grit paper (about 120-250 grit) to smooth it down.
4. Dip sponge in the shellac and run over wood for first coat. Let dry for 10 minutes or until dry to the touch.
5. Sand with a lighter grit paper (250-500), apply another layer.
6. Sand with a VERY light grit (800+) sand paper for a very smooth surface and shellac again.
7. Repeat sanding and shellacking until you're happy the the thickness of the shellac on the wood then polish with a butter (I use some old body butter made of cocobutter, lavender, mac wax, and grapeseed oil).
Store your sponge in the other container to keep it from drying up.
That should give you a nice smooth surface that is natural and non-toxic and surprisingly very quick and non-messy to do! At the very least, sanding your wood with 800+ grit sand paper (you may have to look in automotive stores for this high grit paper used in auto detailing) it will get very smooth and with some oil will likely work better simply because the soap can't get caught in the rough surface of un-sanded wood. Very fine paper is a must for getting the wood super smooth