The candidate would most likely be a priest of the Slovak Church sui iuris or of Slovak descent/ethnicity. There is no sound reason for a Ukrainian to be considered - a Ruthenian from the Metropolia would be more logical as a candidate.
There is no synod or sobor to act and Major Archbishop Husar has neither jurisdiction nor any omophor to exercise as to the Slovak Church.
Candidates will be selected by the Congregation for the Oriental Church, as is the case in all instances of Churches sui iuris of less than metropolitan status/rank.
The Apostolic Nuncio to Canada, Archbishop Ventura, will be consulted by the Congregation and it is possible that the Metropolitan Archeparch of the Ukrainians, as the ranking Eastern hierarch will be asked for recommendations or his opinion, but there is no requirement that such be done. It may, for its convenience, ask knowledgeable hierarchs of Sister Churches to make recommendations for names to be included in the terna (the list of 3 candidates to be considered by the Pope), but it is not required to do so.
Many years,
Neil