How can I find care for my spouse while I get away for a few hours, a few days a week?

Find a "club" for him to go to. By that I mean what is usually called Adult Day Health Program (aka day care). You can sign up for one day a week or five, a full day or a few hours. There are activities, meals, and supervision. They often offer services like toe nail care.

There are a couple of individuals who have offered to come and visit with my husband while I leave for a while. My problem is my husband has never really made male relationships throughout life. He has always wanted to do things only with me. Now, when a male friend would come to visit, he feels as though he's having a babysitter? He, of course, has no understanding of what my needs are or the stress I'm under. Any suggestions as to how to introduce him to the idea?

You can hire a sitter or care giver to come into the home. A sitter can not legally lay hands on ANYONE. A care giver can lay hands on another to assist them, to help them.
You can go through a Nursing Agency to find these people who have certification's. This is what I would do. You can also fine people on Craig's list for this kind of help for I have a friend who use it all the time & he has had good results. I just happen to be an R.N., who wants to have the certification & an overseeing board if things are missing from the home or to go to who over sees, if it is not of my standards.

I also am a care giver-24/7.

Barbara, You are under much stress as a caregiver. To do the best job possible you need to take care of yourself. The first thing to look into is to see if there is an adult day care in your area. They are best geared to help your husband. The next thing I'd check into is ask family to select a day/ time they can help say 4-6 hours . The sooner you get help on board, the better you will feel. My mother in law has 2 friends who give 4 hours= 8hours a month to help out. Are there people from church who could help a few hours?