Hi! Welcome to the forum!
I have a 5month old Sunny so I know where you are with this lol. I got Cal 2 months ago.
All I can say at this stage if you want me to be honest....you're moving a tad quickly lol. Sunny's live for 20-30 years so trying to have him out via force on day 2 really isn't needed!!

The shop owner has done a little damage by using a towel but if you carry on using towels as you normally do and not to touch him with at all until he trusts you (even only then to keep warm after a bath or a vet visit and such like). He should get the idea that the towel is no danger to him at all.
If you must have him out, leave the cage door open for him to come and explore. You need to of course parrot proof the room with no bare windows/mirrors/electrical cords/any danger of an outside door being opened etc. The only snag is getting him back home though. Usually a light weight towel is the answer

in this case though, that'd be horrendous so I really would suggest you let him get more comfortable in his new surroundings first.
Start with sitting by his cage and just talking and going about your daily business. Don't attempt to touch - you need to let him know you're the good guy!
Read him books/sing to the radio/think aloud ANYTHING. Constant chatter is the key! You can try feeding him through the cage with treats but don't be surprised if he runs off.
Make sure he has 12 hrs undisturbed sleep in the dark of a night time.
Just take things slowly and buy a book. Parrots for Dummies is amazing but I love my conure book too which is The Conure Handbook by Anne C watkins. It will give you invaluble guidelines and teach you of all the dangerous foods, do's, don'ts and every day dangers like metal poisoning, teflon(non stick cookware for example) and the pro's and con's of wing clipping if you decide to.
The biggest piece of advice I could give you is to listen to your bird. They aren't like dogs or cats, everything has to be on their terms. Gain trust and be ready with the bandages because they can bite you VERY hard lol. Cal used to jump on my hand and bite me when we first tried step up. Only when she wasn't scared of me and trusted me could I teach her biting isn't acceptable.
I hope I explained that ok!
All I can tell you now is that I got her from an aviary 7/8 weeks ago yesterday (my time flies) and she'd only every been touched by humans twice. Once by the vet and the other when she went in the carry case to come home.
With the help of the AMAZING people on this forum, me calming down and realising there's no rush and LISTENING to Cal she is now a velcro bird who would happily be on me or my husband all day if it was possible. It takes time and patience, but when it happens it's so very magical - I cried buckets the first time she made voluntary contact. She's a brilliant, amazing girl but we had to EARN the privilege of knowing that.
She loves cuddles, preens us, plays games, will sit on your shoulder or any available body part for hours and gets most upset when you leave her behind to go to the loo lol.
Your bird is equally as amazing but please, slow down, RELAX, enjoy the ride and watch as your bird begins to love life. It's gorgeous - honestly!!!!