I would agree with the suggestion that there are ways to be close without actually having to hold if you don't want to. Get a really good bouncy chair (We had the baby bjorn one). Sing songs together (OK so maybe they are not actually doing the singing
), tell stories, have them nearby to talk to while you do errands.
I certainly don't think you should worry if your LO wants to be held at this stage or worry too much about teaching them to be alone. At around 4months they are
just beginning to realise that you are not actually joined together as one person anymore and that they are separate - pretty scary I'd imagine. I would take this time to offer lots of hugs and find ways to 'be with them' while you can still get things done. When Sam was that age I might leave him to lie down on the mat in the bedroom so I could hang up washing. If he cried I would go over and reassure him but I wasn't using a method to try and teach him to manage without me. You've got plenty of time to worry about all that in the future.
Very clingy is the way most new babies are designed. Enjoy it - before you know it they'll be crawling away from you at 90mph and later running and you'll wonder where these few months went.
During A time you could certainly use a paci if you felt that was right and as for holding them during A time - it's called being a mum - not accidental parenting! Think of all those chats Tracy had with babies during A time - songs and stories - when they can't even sit up a lot of your communication time with your baby will be in A time with you holding them or sitting with them.