Do I have to turn off the main water supply to replace tub/shower faucets & screws?
Every shower handle and regulator is a bit different.  

See the picture below which is just an example:



If you are really just replacing the handle - which is really items 1-4 (and sometimes 5-6 or sometimes 5-6 don't exist) - then no you do not need to turn off the water.  But just by the nature of doing this you are probably going to move the stem and get sprayed with water off and on, or just on if I am doing it.

As every manufacturer is a little different there are various reasons why handles get loose.  This example shows a more gears/bushing connection, some manufacturers use a specific shape (square/rectangle/hex) to connect the handle.  

The reason why I not this is sometimes 5-6 is stripped and the handle is fine.  And sometimes 5-6 is really part of the main regulator and as soon as you start moving them water starts coming out of 8.  So if you are sure you are just putting on the handle you do not need to turn off the water.  But once you start touching other things turn off the water and turn on the faucet at the lowest point in your house (this will help drain the lines so you don't get a half gallon of kickback in your walls).  

As a side note: Turning off the water for your house should be a simple process of turning a valve.  You should not be scared to do this and this is good practice as you might need to turn it off in an emergency situation.  All adults living at a house should be OK with turning on/off the water and power to house.  Also the bathroom or shower could have its own shutoff valve.  For a shower this would usually be the floor below and sometimes (not often) under the sink.