My guess is you might be off from diving from 1 to 4 months. The scar on the belly is not a judge of the degree of difficulty it is on the inside. My guess is if it is a clean removal with minimal scarring, adhesion, edema, bile leakage, etc... They will clear you in 1 month.
If there is alot of edema, bleeding, difficulty identifying vessles, inflammation, etc.. The waiting period might be closer to 3 months.
I would not use the scar on the skin as a judge of how well the procedure went. It is up to your surgeon, but I would suggest a minimum of 1 month.