This answer to another question provides a link to the Tutorial for Priests who wish to learn How to offer the Tridentine Mass According to the Missale Romanum 1962 within the Roman Catholic church, which says about sponsors (godparents):
34 To validly act as sponsor it is required:
(a) that the person is baptized, has attained the use of reason, and has the intention of acting in this capacity;
(b) that he does not belong to a heretical or schismatic sect, is not excommunicated whether by condemnatory or declaratory sentence, nor legally infamous, debarred from legal acts, nor a deposed or degraded cleric;
(c) and that the person is not the father, mother, or spouse of the one baptized;
(d) that he is chosen by the one baptized, or by the parents, guardians, or, if these are wanting, by the minister;
(e) that during the act of baptizing the sponsor (or his proxy) physically hold or touch the one baptized, or immediately lift him out of the water, or take him into his arms from the font or from the hands of the minister.
35 To lawfully act as sponsor it is required:
(a) that he has reached the age of fourteen [some more recent sources says sixteen], unless the minister sees fit to admit a younger person for some valid reason;
(b) that he is not excommunicated for a notorious crime, nor excluded from legal acts, nor legally infamous (even though no sentence has been issued to that effect), nor interdicted, nor a public criminal, nor infamous in fact;
(c) that he knows the rudiments of the faith;
(d) that he is neither a novice nor a professed religious, unless necessity urges it and the sponsor has the express permission from at least the local superior;
(e) that he is not in sacred orders, unless he has the express permission of the Ordinary.
So it is not a modern Roman Catholic church requirement for the sponsor to be married or to live locally to the child.
Within the modern Ukrainian Catholic church, the requirements seem analogous: a member in good standing of the Ukrainian Catholic church, not a parent or spouse of the one being baptised, and above the age or reason and moral responsibility. I've also found references (e.g. GodParenting101) that state that
It should also be noted that an Orthodox Christian who has not had his or her marriage blessed in the Orthodox Church is excluded from exercising the privilege of serving as a godparent, because they are not considered to be in good standing with the Church.
but this doesn't appear to equate to a requirement to be (or have been) married.
I haven't been able to discover how the 19th century Ukrainian Orthodox requirements differed from these, but I doubt they were less stringent.
However, for practical purposes, a godparent who lived in the the same locality as the child would be best positioned to fulfil the undertaking they have made to support the parents and guide the child in his/her faith. And a married godparent would probably be viewed as better able to set a good example. It's also very probable that most adult individuals in the community did marry (unless they entered religious orders). So although it wasn't an explicit requirement that godparents be local and married, I'd expect that it was a very likely outcome.