Unfortunately, no.
The IRS requires that if either spouse is under Family HDHP coverage, then both spouses must report Family coverage.
What this means is that the two spouses must share the Family contribution limit of $6,900. That is, the aggregate of all HSA contributions to either HSA must be no more than $6,900 if you are both under 55.
So, one spouse can't max out the Family limit while the other spouse maxes out the Self-only limit.
Sadly, this is not well-understood, and many people end up making excess contributions each year by not realizing this. I am glad you asked first.