In the printer’s manuscript, Oliver Cowdery initially wrote “in the thigh”, which is normal English usage, but then virtually immediately Oliver corrected the definite article the to his (there is no difference in the level of ink flow for the supralinear correction). Of course, the personal pronoun his also works, so there does not appear to be any intent to edit here. Undoubtedly the original manuscript, not extant here, read “in his thigh”. For a list of three other cases where Oliver Cowdery momentarily wrote the instead of his, see under Alma 31:9.
Elsewhere the text allows for either the or a possessive pronoun in referring to a part of the body, for instance, in references to the hair of the head:
It should be noted that in Alma 40:23 the 1830 typesetter changed “their heads” to “the head”. There is one other example referring to wounds and a part of the body; in that case, the text uses the possessive pronoun (just like here in Ether 13:31) rather than the definite article the:
Summary: Maintain in Ether 13:31 the possessive pronoun his in the phrase “in his thigh”, although in modern English the definite article the is normal for this phrase.