In the appendices of the Lord of the Rings books (Appendix E - Writing and Spelling) it is said:
WRITING AND SPELLING
I. PRONUNCIATION OF WORDS AND NAMES
The Westron or Common Speech has been entirely translated into English equivalents. All Hobbit names and special words are intended to be pronounced accordingly: for example, Bolger has g as in bulge, and mathom rhymes with fathom.
In transcribing the ancient scripts I have tried to represent the original sounds (so far as they can be determined) with fair accuracy, and at the same time to produce words and names that do not look uncouth in modern letters. The High-elven Quenya has been spelt as much like Latin as its sounds allowed. For this reason c has been preferred to k in both Eldarin languages.
The following points may be observed by those who are interested in such details.
C has always the value of k even before e and i: celeb 'silver' should be pronounced as keleb.
-The Lord of the Rings, Appendix E (Writing and Spelling).
For example the name Círdan is pronounced "Kírdan" and not "Sírdan". But does this extend to words which are not Eldarin (elven)?
I ask this because when the paragraph talks about the "c" letter, it is referring to Eldarin languages, however the "Consonants" part refers to all languages (it seems).
For example do I pronounce the name "Tar-Ciryatan" with the same "K" sound? Even though he was most likely named after Círdan himself, it is actually a Númenorean name, not Eldarin.