The 16-bit CRC-CCITT in SdFat can be lifted for standalone use. It does not depend on other SdFat code.
The function is declared static but you could remove the static and share the function between SdFat and user code.
The function and table are in Sd2Card.cpp at about line 100.
static uint16_t CRC_CCITT(const uint8_t* data, size_t n)