Hello and congratulations with your conures! I recently adopted a 3 year old Sun conure and also have a 3 year old Green Cheek conure.
Such FUN birds they are!
You didn't say how long you've had your conures but time is of the essence when bonding/taming these guys.
Initially you asked if wing clipping would make them afraid and untrusting of you and my opinion is...not really and most likey NOT for a long term...and you will have a lot more "leverage" with their wings clipped to do some "hands on" bonding. By that, I mean that they won't be able to fly as well so you'll be able to sit on the floor with them and sort of "corral" them closer and closer to you until they are eventually walking on you, or over your hand etc.
For birds that I've had that I've wanted that hands on relationship with, I have clipped until trained then let them have full flight again. My experience was that one wing clip was all I needed...and a lot of time to spend with my bird, to get him/her hand tame.
Just tossing some toys and treats out on the floor and laying there while they mill around you is desensitizing them to your presence. And talk...talk, talk, talk, talk, talk to them, sing, read your book or paper out loud to them, what ever...let them hear your voice and get comfortable with it. I have found my voice to be my best tool, believe it or not.
I have a pair of cockatiels I rescued from a terrible neglectful and abusive home. I've had them nearly 3 years. Because I have other birds, it wasn't high on my list of priorities to have them be hands on handled by me. My first goal was to get them comfortable with me walking into a room with out near fatal heart attacks and risking hurting themselves flapping around their cages so wildly in fear.
Talk, talk, talk, talk to them I did. When they were calmed down with me walking into the room, my next goal was to get them confident that I wasn't going to hurt them while feeding, and reaching into their cage for cleaning.
Then I started opening their cage door and letting them out....and talk talk talk talk talk...to them.
I could go on and on and on...but after nearly 3 years, they are still fully flighted, my male tiel..Charlie has a very extensive vocabulary and LOVES to talk to me. We whistle, I say...kiss kiss kiss and he makes the kissing sound...or he'll say to me...Kiss kiss kiss and I make the kissing sounds...he tells me....I love you! Every single day..melts my heart. He will let me get right up close to him now, he'll even walk toward me to watch me talk to him.
Both him and Sweetpea are "stick" trained, meaning that when they are out and it's time to go to bed, I can offer a stick/perch for them to step up on and put them away and they are excellent with that, but if I offer my finger, they always run off or back away. They used to fly crazy through the house when I offered my finger to step up on, they don't do that anymore.
If they are sitting right next to their dish when I reach in their cage to remove it or add something to it, they no longer move away, but just sit and look at me.
So fully flighted we've made a TON of progress over the last 3 years...but it's been super duper slow.
I'm pretty sure had I clipped them to begin with, they'd be at the very least, comfortable with stepping up on my finger or hanging out on my shoulder. I don't really know why I didn't...other than it wasn't high on my list of priorities with them to have them hand tame.
Now days...I just really enjoy our relationship as it is and every day we are getting closer and closer and, especially Charlie's curiosity is nearly getting the best of him. He watches me handle our other birds and he'll fly really REALLY close to be, sometimes doing laps...like he wants to land on me but still isn't sure.
I just know one of these days....
For you, I'd say it depends on your goals and how much time you have to spend with your conures. And wing clipping is temporary, usually only lasting a couple months, if that and then you can be back to fully flighted birds if you didn't like them clipped.
Good luck with them and post pics! I LOVE Suns!
Toni