Hi Mateusz,
I'm not aware of a way to convert a standalone script to a bound script.
To edit a script that is bound to a sheet, you'll need edit access to the sheet. That's because container bound scripts have the same editor access permissions as their container file (reference:
Collaborate with other developers | Apps Script)
If you cannot have access to the prod sheet, perhaps you can try this: Make updates and test your script using dev. Then share your script with someone who has edit access to prod and have them push changes for you.
Best,
Oliver