They do make 1/8th router bit and table saw blades, buy quality or you may regret it and you will have to take as much time as the cutter will go.
For 3/16, either get that size router bit or use the 1/8 kerf saw blade and run it back to get it to the 3/16.
There are 1/8 routing hand planes to cut that size channel if you are about that life.
Personally, I would use a router table with the right sized bit because a 1/8 table saw blade makes me feel irrationally uncomfortable and using a routing hand plane for anything deeper than 1/8 would be entirely too tiresome.