Hi and welcome! I'm pretty new here too, they're reasonably nice folk 
Here is what I would start out with, (like I said I'm new... so someone may come along and tell us this is not a good approach).
You can change the cursor for each mode to the same graphic, see ChangeCursorGraphic in the manual. Then, let's assume that you've got a gui named MYGUI, and use a button in there which is the current mode icon.
Then:
The right-click mode cycling is done in on_mouse_click (see Script->Edit Global Script).
In there, you'll see (assuming you've got the default function), that if it's the LEFT
button, it processes the click, otherwise, it does SetNextCursorMode().
After the SetNextCursorMode() call, you can put something like:
Code: ags
MODEBUTTON and WALKSPRITE etc are the corresponding integers you set up.
I hope that made sense.
I think the above will do, but like I said, it's just a starting point. You should check out the manual about SetButtonPic to make sure the button behaves like you want (ie, not like a button). I don't know how to do it other than a button though.

Here is what I would start out with, (like I said I'm new... so someone may come along and tell us this is not a good approach).
You can change the cursor for each mode to the same graphic, see ChangeCursorGraphic in the manual. Then, let's assume that you've got a gui named MYGUI, and use a button in there which is the current mode icon.
Then:
The right-click mode cycling is done in on_mouse_click (see Script->Edit Global Script).
In there, you'll see (assuming you've got the default function), that if it's the LEFT
button, it processes the click, otherwise, it does SetNextCursorMode().
After the SetNextCursorMode() call, you can put something like:
int mode = GetCursorMode();
if (mode == MODE_WALK)
SetButtonPic(MYGUI, MODEBUTTON, 1, WALKSPRITE);
if (mode == MODE_LOOK)
SetButtonPic(MYGUI, MODEBUTTON, 1, LOOKSPRITE);
etc....
MODEBUTTON and WALKSPRITE etc are the corresponding integers you set up.
I hope that made sense.
I think the above will do, but like I said, it's just a starting point. You should check out the manual about SetButtonPic to make sure the button behaves like you want (ie, not like a button). I don't know how to do it other than a button though.