Depending on the size of the tanks, they may need to be above some substantial support in the bottom of the floor structure.
My first trailer has smallish tanks (20 gallon) hung under the frame with one welded steel brace under each tank.
My current trailer, once the plastic underbelly is removed, have four welded steel supports under each of the three tanks (fresh, gray, black).
My brother did what you describe to our father's 1986 Shasta. He's familiar enough with plumbing to do the work himself. He removed the underbelly cover, cut the wood braces that held the tanks in place. He then moved the trailer to where he was setting it up. He had the sewer plumbing in place. The vent runs up the outside of the trailer wall. Hooked everything up himself. It is a very simple setup because the toilet is in the middle of the trailer with the wet wall back to back with the kitchen sink.
Now this is a very rural county in Arkansas with no codes except EPA requirements on the septic system. He hooked into his mother-in-laws' existing septic system.
As mentioned above - a local plumber would be the best person to talk to about the necessary conversion.
Most likely you could get by with only removing the black tank. Use the gray tank as is and set it to drain permanently. You will need to use some disinfectant / deodorizer in the gray tank every few days. Stuff producing smells will grow in a gray tank because they never completely empty on almost all rigs. Personally, I'd rather remove the gray tank also.
