I'm a keyboard shortcutter over mouse by preference, it's faster for repetitive use, and whatever lag on a letter I get moving to the num pad will be less then a further movement to the mouse, also, while I can't touch-type, I can touch-type on a num pad so it works for me, and probably would for you with a bit of practice but to each his, her or its own I suppose.

Anyway, a function few people really use is CTRL+F, the find function, and even more rarely, find and replace. You may simply find it easy to, for instance, use the vowel and e thingy, oe, ae, etc, then when your done writing, hit ctrl+f and type in 'Ae' and replace with Ä, and then just quickly sort through them one quick mouse click at a time. Or, make your own letter code, like 'qxe' would be e with an umlaut, qze would be a with an accent, etc, and do a find and replace at the end with those, so long as your self-consistent and limit your personal code to impossible or highly irregular letter combinations you need never do anything but hit the find function, put in the code and the special character once, and hit replace all, done, easy. Q, W, Z, and X are all rarely used and on the same zone of the board, I don't think there are any words at all that use two of those consecutively, pick a prefered combo to use for each 'style' and stick to it and problem solved.