Can I use a 10A light switch with an appliance with a 13A fuse?
The fuse is for your protection, so it's your call.  How much do you value your house and the lives of the people in it?

If you want a safe system, then no, don't put a 10 A switch on something fused at 13 A.  10 A is what we call less than 13 A.  That means in a overload condition, the switch will break before the fuse.  That's bad, since a switch "breaking" can mean various things, like catching fire, emitting a cloud of greasy black smoke, or something else unpleasant.

The fuse, on the other hand, is designed to "break" in a predictable and safe way.  That's the point of fuses.  As the current increases, you want the fuse to be the first thing that breaks.  By it breaking, the current will go to 0, and everything else is saved.