As a left handed person, I feel U, bro.

Go to Cyberpunk 2077 nexus mods and there search for the mod named better controls menu. Enjoy ;)

Hi it is apparentely not a priority on CDRP's list.
Fortunately I have the same problem (since my right hand is not the best one can find in the world) and found a counter-measure to this on other forums (kudo not to me obviously).
You have to edit :
"C:\Users\<your_profile>\AppData\Local\CD Projekt Red\Cyberpunk 2077\UserSettings.json"
Edit the section "group_name": "/key_bindings/SettingsLocomotion" and change the values as shown:
"options": [
{
"name": "forward",
"type": "name",
"value": "IK_Up",
"default_value": "IK_Up"
},
{
"name": "back",
"type": "name",
"value": "IK_Down",
"default_value": "IK_Down"
},
{
"name": "left",
"type": "name",
"value": "IK_Left",
"default_value": "IK_Left"
},
{
"name": "right",
"type": "name",
"value": "IK_Right",
"default_value": "IK_Right"
},
you may change everything to your taste but here is the answer to your main problem.

DO NOT FORGET TO:
1/ make a copy of this file first (add the extension bak or old or whatever you like to the original one, so you can restore it to initial state if you mess up)
2/ change the file attributes to read-only so it won't be overwritten by some update of some sort.

Worked like a charm for me.

I'm having exactly the same problem. I tried the solution of Loute44.

But it didn't worked to me neither. =(

Rebinding is working now. SUPER! I knew you can do it!
Turns out that the Grab key (F) is hard-wired. BOOOOOO! I swear they have hired the same person who designed the Fallout UI.

So, I sneak up to somebody, right hand leaves the arrow keys, searches for the F key, then the R key, then the arrow keys again ... looting the same.

As a leftie, you have to own a programmable keyboard.