Yes, you can. It's the number 7414 which tells the purpose of the chip.
The C-letter means it is cmos-type (and it needs to be in your circuit,
as you mentioned), and H means it is high-speed-type. It is not
mentioned to be necessary in your circuit, but it is ok to use the
high-speed type, although not necessary.

ps. according to the datasheet, 74HC14N is Hex Inverting Schmitt
Trigger and 74C14 is Hex Schmitt Trigger.

Both ones are inverting. There are mistake, or maybe the maker of the
datasheet of the 74C14 has considered the "invertingness" a "special
feature" which wouldn't be necessary to tell on the header.