participation of a physician in execution of a capital punishment

In brief, gentiles are also commanded on a system of justice, and a gentile who violates one of the 7 Noachide commandments can be sentenced with capital punishment. (See details in Rambam Hil. Melachim 9:14)
Thus, a physician would be permitted to participate in such a court ordered capital punishment if there was a witness to the crime. According to some authorities, testimony of relatives and the criminal's own admission also suffice. (See Minchas Chinuch #26, #192 and sources in Frankel Rambam ibid.)
However,  circumstantial evidence alone would not suffice.
Regardless, a Jewish physician may not participate in a government ordered execution of a member of his faith.
Kol Tuv,
Meir Orlian