NO!!!!! The wiring is supposed to be rated to the breaker, which will trip if the load is too great (the breaker should be the weakest link in a circuit). If you change the breaker to a 15 amp (but leave the old wiring), the smaller wiring can overheat & cause a fire before the breaker trips.

I'm sure someone will chime in with more expertise & technical info but I've done enough electrical work in my house to know this is a basic.

It depends on the existing wiring. If the circuit in question as at least 14 gauge wire, it can handle 15 amps safely. If not, you are creating a potential fire hazard. This is not something you should guess about. Unless you can verify that every wire in the circuit is rated to handle 15 amps, you should not replace that breaker. If you aren't familiar enough with electrical wiring to determine that, then it is time to call an electrician.

How old is your house?
Even hair dryers run more than 10 amps these days.
Is it EVERY BREAKER that is 10 amp? Or maybe just the overhead lights? Mmmm, you did say that ALL of them are 10.
Most strange. Do you know what amperage your power supply is? 100, 150, 200 amps?

If you are not flipping breakers every time you run a hairdryer, or the microwave with the coffee pot and toaster, and if there is room in your breaker box for another circuit breaker, why not call the electrician to put in a new 20 amp breaker to run your saw and any other power tool of ordinary size?

You might want to post this question in the wiring forum.

Here is a link that might be useful: Wiring forum

Every breaker has 10 amps stamped on it, but a couple of them take up the space of two breakers. In the two years I have lived here, I never tripped a breaker until I used the small compound miter saw. The toaster oven and the microwave are plugged into the same outlet and I often run them at the same time. I'll try the wiring forum.