Things to consider:

Guitar players are people first. They just know how to play the guitar. Approach them as you would approach a mechanic or a plumber. "Hi. I need some work done and I wonder if you would be interested in it?"

This is important for us to know. Do YOU play? You said you don't play guitar. Do you play keyboards or anything? Do you have a music background. That would be helpful in the long haul as far as basing your decisions.

As far as knowing who to ask, when you contact them just ask for clips. You are a boss interviewing applicants.

If you don't like their track, tell them gently, something like "Hey, that's good for a first pass. Do you have any other ideas, possibly something in a completely different vein?" And this is where your music knowledge would come into play. "Maybe you can start on a higher octave and work back down from there", or "Maybe you could cut the timing of the phrases in half". Keep in mind, it's your song. It may be as simple as "Can you give me something like "(and here you hum or doo doo doo doo what your mind's ear hears)?" Or "Can you base that solo a little more on what the melody line is?" Whatever you do, whatever you say, speak with a smile. Always give positive suggestions and energy or the guy will tell you to buzz off. You can also use those generated parts you say you don't particularly like as a baseline. Send him the tracks and tell him to use this as a starting point and "send me some ideas". Ask for 5.

I work with Rog in England quite a bit. He gives me his thoughts, I listen with an open mind, and unless it is totally out of left field (and it rarely is) we tweak and work with it. He once completely retooled one of my songs and it turned out to be as good a pop tune as it was a country tune. Fortunately we both understand who owns the song and who gets the final say. I think we compliment each other pretty well. When he had a lot of vocal students they did a lot of singing and reworked 4 of my songs completely. His kids got experience, I got another set of ears on what I wrote, and I grew as a writer from it.

The key is mutual respect. Everybody works from a different level and a different knowledge base. A guy with a Masters Degree is going to know more about the core and roots of the music, where someone with less exposure plays it by ear. Both ways work, it's the difference between someone with knowledge of cars who knows enough to change oil and a guy who builds engines. Just don't become intimidated or settle for something you don't want. This is your recipe. Use the brand of sugar you want.