Them not being vaccinated means they are at higher risk of getting sick. If your chickens are vaccinated it should help protect your current chickens and maybe they’d act a bit sick for a few days, but the new chickens would be more likely to get really sick. I’d recommend quarantining your new chickens for 2 weeks before you introduce them to your flock, it means if they do have any illnesses they’ll show before you introduce them to your flock and make your flock sick. Id them put them near your other flock for a week so that they can see each other and not interact it should help a little bit with introducing them to your flock. The way I’ve always introduced my chickens is by letting them free range in my chickens space, or by putting them in my run with my chickens. There will be pecking and it can look quite violent, but it is perfectly normal. Unless they are drawing blood from the other chicken, or plucking out lots of feathers leaving bald spots, it’s best just to leave them. You also need to make sure you have plenty of food hidden in places they can’t really see (behind a plant pot or something). Make sure you have plenty of water and food sources, and make sure your new chickens are getting enough.