The word “schedule” can be somewhat confusing, even for native speakers. The reason is that it is pronounced differently in the UK and in the US. In the UK, the prevalent pronunciation is /ˈʃɛdjuːl/ (shed-yool), while the prevalent pronunciation in the US is /ˈskɛdʒuːl/ (skedzh-ool).
However, there is a lot of variety, even when American and British dialects are considered separately. Some Britons pronounce the word with “skedzh” at the beginning, and the final “ule” is often reduced to just /ʊl/ (short “oo”, as in “book”) or /əl/ (“uhl”) in American English. To summarize:
US: /ˈskɛdʒuːl/ (skedzh-ool), /ˈskɛdʒʊl/ (short “oo”) or /ˈskɛdʒəl/ (skedzh-uhl)
Perhaps it will help you remember the British pronunciation (which may sound unusual to someone unaccustomed to it) if I tell you that “schedule” is distantly etymologically related to the English verb “shed”. However, the common root is the Greek word skhida “splinter”, which contains a “K”…
The word “schedule” itself was borrowed into English from Old French cedule (no “K”), which, in turn, is based on Latin schedula (pronounced with a “K”). It seems that it is not possible to argue that any variant is etymologically more appropriate than the other.