When playing thief 1 there is a slight problem with hotkeys: you have one key for running forward, one for walk and then you have speed toggle which in fact makes you creep but not run as usual.
Game doesn't offer you the option to run when pressing shift key, which is customary in most fps.
I was looking for a solution for this and didn't find a nice post yet so i'm writing it here.

In the game create a new keyboard file save under options>controls>customize controls, then click on Save.
Go to your thief gold installation folder and find \SAVES\ directory, there open a file you just created with notepad. It will be named cfg0003.bnd(that is if this is your first save you made, otherwise the number will be higher). Basically just open the latest created.
Inside locate 'bind shift' and change it to 'bind shift +runon' - this will make you run instead of creep when pressing shift key.
You can then set 'bind ctrl +creepon' to creep when you need it, can do this even inside the game.
Afterwards you will set 'w' as walk inside the game and you have controls as in thief 2.

Sorry that i don't use TFix?

well, you should.

In nearly 18 years of playing Thief I've never used the creep button (ok maybe in the beginning). Crouching and tapping forward has the same effect as far as footstep volume is concerned. So you can bind shift to run and then I use middle mouse for toggle crouch. With these two combinations (walk, run, crouch walk, crouch run) you can get most speeds required.

Certainly levels with haunts and tiles in them are easily doable with that combo.