Are you asked if a word ended in (for example) -kha? or -lha?
Yes exactly (and I apologize for the confusion), nominative singular feminine nouns of non-Polish origin ending in (for demonstration purposes) "-aha", "-bha" etc...as well as the examples you gave, "-kha" and "-lha" etc. My question was if their singular dative & locative declensions would still be "-asze", "-bsze", "-ksze", "-lsze" etc.
So far, I've found only one declinable nominative singular (more specifically, virile category) noun ending in "-(not -c-)h"...that noun being "Druh" (nominative & vocative plural "Druhowie") which is apparently considered an obsolete/outdated word