If you have a screen protector on the screen, try touching a wipe of the type that you're going use to a tiny corner of the screen, for about half a second. Wait about 15 minutes. Then get the screen set to that spot is white and see if there are any marks. If there are, there's something in the antibacterial compound that's going to damage the screen protector.
If you don't have a screen protector, you cn do the same thing, but damage would be to the glass, not to a cheap screen protector.
(The odds of an over the counter antibacterial wipe having anything that would damage either the screen or a screen protector are extremely close to zero, but no guarantee.)
BTW, touching a lamp post or tree out in the street is probably more dangerous, bacterially, than a friend holding your cellphone. Thousands of hands have touched them, and you don't know where they've been either. (The same holds true for your car door handle, a seat on public transportation, a library book ... the only way to be completely safe is to be dead. And the more non-serious infections you're exposed to as a child, the better your immune system works as an adult.)