As noted in that post, Canon 984.2 of the 1917 Code basically stated: "bodily defective men who, on account of debility cannot safely, or for reason of deformity with due dignity, engage in the sacred ministry of the altar" are irregular/impeded from the reception of orders; more significant defects, which have the same effects, impede the exercise of orders already received. Notice the two factors which come into play: safety and due dignity. A bodily defect which hiders or prevents either or both results in the irregularity. A defect which does not hinder or prevent safe and/or dignified ministry of the altar does not result in an irregularity.
Addressing the notion of "due dignity" in the ministry of the altar, a commentary on the 1917 Code said:
Becoming performance (of ministerial acts) requires two things: (1) that the faithful are not disgusted or offended by reason of the physical defect of the person performing the sacred act; (2) that by reason of the deformity liturgical laws are not violated in a matter of importance (Buscaren-Ellis, 3rd ed., p. 423).In general, if a man is unable to observe liturgical law "in a matter of importance", then it is possible that he cannot carry out the ministry of the altar with "due dignity."
Now, to the specific topic at hand (see what I did there?): I have heard people refer to "canonical digits", meaning the two thumbs and two index fingers. Look through the old Code, though, and you won't find specific reference to the thumbs and fingers. Looking through the standard, English language, canonical commentaries on the 1917 Code, I haven't seen a reference to "canonical digits." Where was this term used, if not in canonical commentary? Where did it come from? I don't know.
At any rate, in the older form of the Mass, the rubrics specifically instructed the priest to hold the Host with the thumb and index finger of both hands. (In the "new Mass", by the way, the rubrics say only that the priest takes/holds the Host; nothing is said about fingers or thumbs.) Here we see the requirement to use the thumbs and index fingers of both hands. Clearly, a man who doesn't have both thumbs and both index fingers would not be able to observe liturgical law. One commentator on the 1917 Code had this to say:
One who is minus a hand or a finger which are necessary for handling the sacred species, is irregular. This is the case if thumb and index finger are missing. In cases where the hand was complete, but a great stiffness of the arm, caused by apoplexy or paralysis, rendered the breaking of the host or the making of the sign of the cross impossible, the S. Congregation denied a dispensation (Bachofen, vol. 4, p. 480)Just because a dispensation was denied in that case doesn't mean it would never be granted. When a request for dispensation is made, there are three possible answers: "no", "yes", and "there is no irregularity." Each case is addressed on its own merits and there can be changes in perspective over time. As a commentary on the 1917 Code says, "there is no accurate list of bodily defects which bar a candidate from the priesthood, but each case must be judged on the candidate's ability to perform the sacred functions safely and with becoming dignity." (Woywod/Smith, vol. 1, p. 948).
Along those lines, I can point (no pun intended this time) to two cases where a dispensation for this sort of deformity was granted.
First, in 1918, Sacred Congregation of the Sacraments dispensed a man who lost his entire right hand in the war. He had artificial hand and proved that he able to carry out the rites required for Mass. Since he was so able to do this, he was dispensed from the irregularity (see CLD v. 1, p. 485). I'm no expert in artificial limbs but I doubt that this priest could actually hold the Host with the artificial hand. Nevertheless, he was dispensed.
Years later, in 1955, a man who had "mutilated" left thumb (the portion above the knuckle was missing) wished to be ordained. The Congregation instructed his bishop that a dispensation can be granted but the man should obtain a gold/gold plated cap, if possible, for the thumb (see CLD v. 6, pp. 585-586).
(Another case, exceptional in more ways than one, is St. Isaac Jogues.)
Having said all this, I suppose I should answer the question from the beginning of the post: the current law says nothing about bodily defects which result in an irregularity (unless we are talking about self-mutilation). If a man is missing thumbs or fingers or even a hand or arm, he is not "irregular." Rubrics (for the "new Mass) do not say that the priest has to use his thumbs and index fingers to hold the Host. (He simply needs to be able to hold the Host, somehow.)
What does all of this mean? It means that whether a man with this sort of disability is ordained or not depends only on the decision of his bishop (or major superior). The bishop (or major superior) would make this determination based on the man's ability to carry out the priestly ministry (at the altar and otherwise).