You pretty much have three choices, repair the damage you caused removing the A/C components, or strip it down and make it a heat-only system, or strip it down further and make it a blower-only system. If you've bypassed the heater core already then you are on the way to the third choice.

I have air on my convertible. Other than the inevitable pain to service issues, I enjoy it.

No matter which route you choose, you will need to close off all the openings through the firewall.

Merv is dead on...it will never be as good at venting as a non-A/C car. If you install kick panels for a non-AC car it will help, but the dash ventilation will still be lacking.