edit: in answer to your question directly: yes, you would need to navigate via touch.
you would need to use a series of adapters to connect a mouse, since MHL comes through the micro usb port. a cursory google search (less than a minute, if it exists, it's not common) revealed that there are no micro usb male -> female usb-a/female micro usb split cables.
you may be able to get away with:
otg
split to double female usb-a
put the mouse in one
put a usb-a male to micro female in the other
put the MHL adapter in the micro female
i remember daisy-chaining things like that to get video/audio to work with some of my theater systems. but i have no idea if the port is strong enough to do it, or if android would know wtf to do with it if the port could power it.
if that doesn't work and your touch screen is borked, you're done. back up to the googles next time. if your touch still works, you can do it, though it may be difficult. and still back up to google, or write them all down.
remember, phones are NOT that secure, you need to back up your contacts and such regularly. passcodes and such are great at keeping intruders out, but they rarely stop a hammer from messing your life up if you have everything stored in a single location.
