There a number of different thing DNA encodes for including protein structure, and gene regulation. There are also what is called "Untranslated Regions" with no known function, and thus a high degree of variability in structure.
For the DNA that encodes for protein structure, all Human proteins include up to 20 (or 21) Amino Acids, with a specific DNA to protein correspondence. This would be true with all cells in the human body. There is, however, a 22nd
amino acid, Pyrrolysine
that is found in some bacteria, but not in humans.
All cells in the human body also have essentially the same DNA, although it is likely that there will be at least a couple of spontaneous DNA mutations carried by individuals. Hardly enough to be picked up by DNA fingerprinting. There has been some discussion of a Chimera in Sci-Fi literature. Essentially it is a special case of conjoined (or Siamese) twins, in which a single individual is born, but having the DNA of two siblings (which would be highly related DNA).
I believe current Gene Therapy is an additive process in which viruses are used to add DNA to cells. If the viral host is cell specific, then the therapy can be cell specific. Or, perhaps it could only be applied to a single organ. As far as the Untranslated regions, and DNA fingerprinting, it would not necessarily get rid of a fingerprint, but perhaps could be used to add additional data to a DNA fingerprint, and thus confound the results.
Bone Marrow transplants are a unique form of transplant in which one essentially permanently replaces the cells that form blood with those from another individual. And, thus, also would replace any blood based DNA fingerprinting. It can even change a person's blood type. It is a brutal procedure with a very high mortality rate, and thus would unlikely be used as an elective surgery. But... say a criminal with leukemia might get a "new identity".
One thing about a bone marrow transplant is that once completed, the individual will start recognizing the donor's tissue as "self". So, there would not be any need for anti-transplant rejection medications. Presumably, after a bone marrow transplant, one could transplant any tissue from the donor without risk of rejection. An oral swab may not be fooled by a bone marrow transplant. However, one might be able to also transplant some of the donor's muscle into the inside of one's cheek that would then mucosify (apparently it is relatively easy to get tissue to mucosify in the mouth), and one may not need to transplant the actual mucosa. But, one could presumably get enough oral mucosa to fool the DNA tests.
Can one do a testicular transplant?