Well I had to post this, even though most people won't do it. But I made a Breton healer/Illusionist and she is a a lot of fun. She isn't really a pacifist so it is isn't the 'no kills in stats roleplay'. She is a healer because of her pregame experience and she is a little, weak bodied but wise and strong minded woman who has the heart of a lion and the body of a kitten. I mean come on just look at the Breton females, are they not made to be healers or mages? Sure I have some that are tanks, but the natural inclination by appearance it not to be a fighter.

In fact I made her shorter via the console. And then comes Jordis. I made her taller so she looks about 6'4" and my PC looks about 5'1". Jordis killed a giant and two mammoths at the same time while I healed her. Meeko, who tags along, is a distraction for enemies while Jordis is working on the rest. I gave her a bunch of great equipment as, of course, I am also a great enchanter, and she can kill anything on the board, like Draugr Death Overlords, and her health barely even goes down.

My PC does occasionally beat on stuff with her well enchanted sword, but so far has put perks only in Alteration, Illusion, Restoration, Enchanting, and one in steel Smithing. So long story short you should try one. It is a different way to play and change things up a bit.

I've been thinking about a non-combat character, but since it's not possible to play the game without killing anything and support spells in Skyrim are limited to healing and Courage, i don't think that it would be much fun in the long run.

I was afraid of that too, which is why I didn't do it for so long. But I have been enjoying it quite a bit. She is around 35th level and has done the Mage's guild and is trying to develope her dragonborn abilities under the tutelage of the greybeards. Since I have done the MQ so much I rp'd that she distrusts the blades and Delphine so she left her after getting the horn of JW. She will soon realize that she needs to go back to Delphine though.

She is not a pacifist so I don't know if I would call her a non combat charcter. She just lets Jordis do the hacking for her, They can't stand evil doers and bandits so she is pretty combative. She has quite a few kills in her stats because sometimes Jordis' go on hers. She also will take a hack or two at something, especially when she is filling soul gems, she polishes them off after Jordis beats them down that way I can devote Jordis enchanted weapon solely to damage. She also uses her shield to bash stuff to help Jordis out, and keeps her heal spell in her right hand. She paralyzes, calms, etc stuff too while Jordis is fighting. Oh, and when stuff goes to a knee Jordis will quit attacking them so I will often finish them before they get up and smack Jordis in the back. She really quite adores Jordis.

Instead of making her a pacifist and doing the no kill thing, essentially I just use RP that she is not physically strong and becomes vilently ill when channeling Destruction magic. That way I can play her as I am. I have also limited her smithing under the assumption that her lack of strength makes it impossible to progess any further. It is 40 something now and will only go up if I find more equipment to fortify for Jordis.

I am thinking that eventually she might start meleeing after she has perked out all her best mage perks. Right now though I like playing her like this, as I have a bunch of melee magic characters already.

My Raksha is an archer, but there are situations where I play somewhat similar like you.

In bigger combat I play as a healer for Kharjo, as he is the only one in our team who can take some beatings. Often I just don't try to engage opponents but I take care of my team by healing them or taking enemies off them if I see that someone is in trouble. And it's really a lot of fun

I have yet to try using paralyze though.

If you are doing well with Illusion spells to occupy some of multiple enemies I would have to suggest just stick with that. It seems like when I paralyze stuff Jordis will barely attack them. I took it because she was already really good at alteration and had the perks for her shield spells but I wouldn't advise trying to develope alteration and spend perks on it if you are doing well already.