if the new guy is right for you, he'll still be right for you when the divorce proceedings are over. Lots of people do date before the proceedings are over, but most don't even contemplate trying to meet or date till after the separation.
Turning your husband into a cuckold is not a way to get him in the mind of negotiating anything amicably. Your lawyer is thinking of the process of getting this over with, without turning the expense of it into something bigger than your combined assets would justify. The less amicable it is (because your husband is motivated to be less amicable because of the constant reminders of your cheating), the more expensive and painful and LONG LASTING the divorce will be.
If you want ti over with as simply and cheaply and quickly and happily as possible, then follow your lawyer's advice, and trust that your new relationship is strong enough to survive a few months of separation. If you can't trust it that far, then it's not much of a relationship... certainly not one worth breaking up a marriage over!