I know how to exclude all HCEs from receiving the SH contribution. I know how to exclude a "class" of employees from participation, but here's the question. Is it permissable to allow an HCE (the owner) to make deferrals but not receive the 3% sh? We don't want to exclude all HCEs because there are other nonowner hces.

I have worked with many plans that specifically excluded owner HCEs from a particular contribution type while allowing it for non-owner HCEs (or vice versa). It depends on the type of document and the type of allocation formula. If you're using a prototype document or have not previously been doing 401(a)(4) testing there may be other considerations.

It is allowable to do so, exclude some HCEs from SH and not others. Some prototype documents have a section where you name exclusions by contribution types and by employee class.

Is the idea that he wants the flexibility to put in a contribution for himself in some years and not in other years?

It would be unusual to prefer deferrals which are subject to payroll taxes. The Safe Harbor Contributions are true employer contributions and not subject to payroll taxes such as medicare tax.