Harding’s father had 8 children so there are likely plenty of 2nd and 3rd cousins around, he should get a 23andMe DNA test which can provide relative names that have also been tested and who consent to identification to other family members.
Probably already has and it doesn’t mention Harding and just says Satan.
Harding had one brother and four sisters who lived to maturity. If any of them have living descendants, DNA could be obtained from them. If not, there are probably more distant relatives whose kinship to President Harding is well documented who could be tested.