Segwit addresses are not derived from legacy addresses. However a legacy address can be derived from a private key for a segwit address, and vice versa. Private keys are just numbers and are not locked to a specific type of address that they should be used to create.

Note that Electrum uses a special format for private keys in order to indicate what type of address they should be used for. You will need to export those private keys and convert them into a format that your forked coin's wallet can understand.