Would it be better to use HKDF or SCrypt for deriving a child key?
SCrypt is a Password Based Key Derivation Function or PBKDF. In general you don't need such a function if your input is already a key. In that case you need a Key Based Key Derivation Function - a KBKDF.

Currently the best KBKDF is probably HKDF. This can take a key (e.g. the public key), info (e.g. $i$ or the hash over $i$) and possibly a salt. As it is based on HMAC, there is little need to perform any hashing in advance (so using a specific encoding of $i$ would suffice).

For key material where the bits are fully random you may also just use HKDF-Expand (the first part of HKDF, HKDF-Extract just compresses the random bits in the key material in case they are not well distributed).