Early Noldorin
muig
noun. cat
gwag
adjective. soft
There are more words but they are from Tolkien's earlier conceptional periods. Tolkien likely changed these words as he evolved the aesthetics and completeness of the languages. You may even find languages that Tolkien later rejected. Do not mix words from different time periods unless you are familiar with the phonetic developments.
Below: Tolkien's Late Period (1950–1973). These are from Tolkien's late conceptual period — his most settled forms of the languages. Prefer these over the earlier ones above when composing new text.
The word ᴱN. muig “cat” appeared in Early Noldorin Word-lists of the 1920s (PE13/150). In the Gnomish Lexicon of the 1910s, Tolkien instead had G. {mio >>} miog “cat”, along with masculine and feminine variants miaug or miog “tom cat” and {miauli >>} miaulin “she-cat”. The derivation of these early forms isn’t clear.
Neo-Sindarin: I would retain ᴺS. muig “cat” for purposes of Neo-Sindarin, derived from ᴹ√MIW “whine” via an abnormal vocalization: m(i)wikē > mu̯ike > muig. Elaran pointed out that a more normal development would be ✱mŷg < miukē.