I don't think there's a way to re-bind the keys, but you can either left-click on a menu item, or you can use the F1, F2, F3... keys to access the different menu items, like "use" or 'talk."

There's also a mouselook patch (https://github.com/JohnGlassmyer/UltimaHacks#ultima-underworld-the-stygian-abyss) which I highly recommend that creates some new keybindings. [E] will "use" an object, like a door or a person (that allows you to talk to a person) and [Q] allows you to look at an object. The [`] key will allow you to switch between having your mouse centered on the screen where moving your mouse will move your POV, and moving your mouse around to interact with inventory items. There are some other very useful keybindings that come with this patch as well. It takes a little effort to install the patch, since you'll need to unarchive the game.gog file, patch the executable, and then compress all of the game files back into a new game.gog file with the new, patched, executable. But it's well worth it.

To use a key on a door, you'll need to "use" the key, which will change your mouse icon to the key, and then you can move the key icon on a door in order to use the key on the door.

RTFM if you have any issues. The Ultima manuals back in the day were super essential reads! Very difficult to play without reading the manuals.