You have quite a few things there. The first is your medical condition, is it something that will be fixed at some point or permanent? That really decides if you just tough it out a bit or look at other options.
There is the issue of "you" before discussing anything with your wife. Are you going to be able to deal with the potential outcome(s)? Before you ever talk to your wife you need to wrap your head around all the directions things could go. I mean literally treat it like work, pen and paper and brainstorm it out in a flow chart, it could go many ways and once you open the door you have to be alright with all outcomes.
Best case scenario: She could hear you out , agree and find a man to only have sex with her. Clean, not interference with your daily life. You live happily ever after as a married couple with her only having an encounter on an as needed basis with one man who is good with himself being in that role forever.
Also possible:
She freaks out and gets super angry at thought of you telling her to "sleep around" , she gets over it or doesn't and leaves you.
She agrees with you that she needs sex and you are not able to provide it decides that the issue is significant enough you proposed this and concedes it is time to move on.
She agrees with you that she needs sex and you are not able to provide it and starts having sex with another man and the sex is really good, your marital sex has not been for a long time so she goes overboard having sex all the time and it impacts your marriage.
She agrees with you that she needs sex and you are not able to provide it and starts having sex with another man and falls in love and it impacts your marriage.
She agrees with you that she needs sex and you are not able to provide it and starts having sex with many men and likes it and it gets out of control and impacts your marriage.
She agrees with you that she needs sex and you are not able to provide it and the hotwife lifestyle becomes her thing and you get cucked and she does whatever she wants.
There are a ton of other possible outcomes but really only one that I think suits your "plan". Is it possible, yes. You might have the optimal outcome but please prepare yourself for all others before discussing with your wife. If you decide on this route be fully aware that you are going to undergo a lot of stress. I don't know if you fall under the "let her go do her thing" or if you would be present. Neither is easy. Myself I happen to have a particular type of perverse desire of watching. My thing, maybe not yours but it is what led me here not medical issues. In my case I . have a fetish, watching. You will need to know what you want. If you do not care to watch consider at least going with her for safety at first. A hotel is safe and neutral ground. You can remain in your car or elsewhere if you choose. This keeps the guy away from your home. Also understand that things change. If you source the right person it may be great for a bit then change. Try to always have an exit strategy if it is going to be a sex only thing, so you can end it easily if needed. Emotionally you have some work ahead of you. The big hurdle is of course doing this the first time but then afterwards you both will have feelings to deal with. That is an area you need to brainstorm based on you, your wife and your marriage.