I dont know how much pressure you are dealing with but if those vessels are considered pressure vessels forget the idea. If they are just vessels under hydrostatic pressure from the content you could probably do it legally depending on the state requirements. In Massachessetts tanks w/ capcity of 10,000 gallons and over containing products other than water have to be inpected yearly and tanks must be build per API, ASME or equivalent codes.
The procedure that you are recommending to weld both tank w/ a strap on the outside would not be allowed if tanks were considered pressure vessels primarily because of the
longitudinal stress creating a moment at the joint and also because of QC issues.
It tanks are atmospheric tanks review API codes.