I'm making a platforming game based on physics with wall walking. The current control scheme is very simple.

Jump = Spacebar or A (Nintendo Controller) / Right mouse button

Jumping will also detach you from a wall climb.

Move left and right = A an D on keyboard or the left joystick. You can also hold the mouse in front of the character then hold the left mouse button and the character move towards the mouse.

I personally think the mouse controls are the easiest and most intuitive. I'm mainly looking for feedback on the keyboard and gamepad controls. I originally had it so when the character was climbing a wall or upside the controls would change with direction. However I got tired of switching between up and down and left and right on every turn. I found only 2 keys a little easier. This way no matter which way you're moving you simply press the opposite direction key to move the other way.

Here is a link to a playable web demo. Please let me know what you think.

https://joyful-squirrel.itch.io/skiethesnail

Cute game... this walking on the ceiling business reminds me of the old DOS game Crystal Caves :)

The controls are fine for me, but I'm an avid keyboarder and I've encountered this exact mechanic before. I would include an option to switch between control styles, since I think some people will be frustrated by pressing left to go right. It sounds like you already had it set up for "absolute direction" already, so if that could be toggled then I bet at least some players will prefer it. 

Some other notes that you didn't ask for :P

• The movement speed is pretty slow IMO. And, if you were going to adjust it, now would be the time since doing that later could break all your levels.
• The variable gravity thing was a little confusing. You did do a pretty good job of showing stuff in the tutorial with just animations. But I still found it odd that the gravity would change with the surface I was standing on (that is how it works right?). Maybe some additional indicator of which direction gravity is going would be helpful?
• The music is cute but a little intense. Based on the visuals (which are great) I would have expected something more relaxed.