I'm not sure how helpful this will be, but I have a few observations:
1)There is a city called Trenc'in and a (former) county that was named after it.You might just have the name of the county he was from.
2) The surname is spelled Hunc'ik in Slovakia today.It is pronounced "HOON-cheek."Prior to WWI, it might have been spelled Huncsik, which gives the same pronunciation according to Magyar/Hungarian spelling rules ("cs" in Magyar is like "ch" in English).Here is a listing of the places in Slovakia where people with that surname lived in 1995:
Priezvisko HUNÈÍK sa na Slovensku v roku 1995 nachádzalo 62×, celkový poèet lokalít: 21, najèastejšie výskyty v lokalitách:
OCHODNICA, okr. ÈADCA (od r. 1996 KYSUCKÉ NOVÉ MESTO) – 8×; KYSUCKÝ LIESKOVEC, okr. ÈADCA (od r. 1996 KYSUCKÉ NOVÉ MESTO) – 7×; POVAŽSKÁ BYSTRICA, okr. POVAŽSKÁ BYSTRICA – 7×; NOVÉ MESTO NAD VÁHOM, okr. TRENÈÍN (od r. 1996 NOVÉ MESTO NAD VÁHOM) – 5×; ŽILINA, okr. ŽILINA – 3×; DUNAJSKÁ STREDA, okr. DUNAJSKÁ STREDA – 3×; KOTEŠOVÁ, okr. ŽILINA (od r. 1996 BYTÈA) – 3×; KYSUCKÉ NOVÉ MESTO, okr. ÈADCA (od r. 1996 KYSUCKÉ NOVÉ MESTO) – 3×; MAKOV, okr. ÈADCA – 3×; ŠAHY, okr. LEVICE – 2×;
3) I can't find an occurrence of Capay as a surname in Slovakia.It may have been spelled Czapay (the Magyar spelling) or Czapaj or even T'apaj.
Do you know if the couple married in the Old Country before emigrating, or did they meet and marry in America?If the former, they would have to have come from the same places or nearby places.
The tradition of working with wire as an art form or as a way of repairing household objects was strongest in northwestern Slovakia, which would include the northern reaches of Trenc'in County.