No.

It is part of the trade-off you make for the formal Household Account wrapper benefits, in return for having pooled access to the combined Avios points balance of all members of the household in their own accounts, you can only spend them on HHA members.

If your BA Executive Club account is not part of Household Account, then you can spend your own on yourself and/OR anyone else.

(Subject to the usual restrictions that you can't sell them, etc).