Can You Reduce a Gummy Smile Without Doing a Surgical Procedure?

Depending on how severe the gummy smile is, surgery may be the only option. If that was a desire from the first surgery, it should have been clearly stated, as surgery for an overbite normally has zero effect on a gummy smile. It is possible that the surgeon's only goal was the overbite.
If the gummy smile is extreme, Botox will have very little effect. SOME, but perhaps not as much as desired. Lip tacking or lip lengthening surgeries are moderately successful, as quite often the results are not as dramatic as hoped. Soft tissue solutions for hard tissue problems are known for being unpredictable.
If the roots of the teeth are long enough, a crown lengthening procedure may be an option, but that is still a surgery. This is where bone around the teeth is removed, perhaps 2 mm, and when the tissue heals more teeth are exposed. This WILL make the teeth look longer, so if they are already the right size, then another surgery should be considered (like having bone above the teeth removed, like a Lefort Osteotomy).
I suggest a consultation with a few surgeons and periodontists to see what would work best for you. If it is minor, laser gingivectomy might be enough.

Difficult to do without surgery.  Botox can work but lots of people end up looking distorted but it only lasts 10-12 weeks and gets very expensive over timeLaser surgery is ok for minor exposure but if major you can do a reverse vestibuloplasty.  These are minor surgeries compared to jaw surgery.Since you don't want surgery widening the arch with a DNA Appliance can usually correct the problem but this is not inexpensive.  The inexpensive alternative don't smile to large.  I have patients who practicew how they smile to control gummy exposure.  Not the best solution but inexpensive and no surgeryIra L Shapira DDS, D,ABDSM, D,AAPM, FICCMO

The best way to reduce a gummy smile would be with  laser removal of the excess gum tissue. In addition, you could have some Botox placed under the nose around the muscles that raise the upper lip to help keep your lip from raising as far when you smile.  Good luck.