I think it depends on how tame, or not, your doe are. If they are not tame, you might risk them abandoning the fawn, because you have spent too much time handling it, and you need to consider the amount of stress on the doe and fawn if you are in there messing with it part time. If your doe are fairly tame, just spend lots and lots of time in the pen, giving treats. Fawns mimick mom. If she is tame and comes towards you (or at least doesn't flee) when you enter the pen, so will the babies. Fawns I let the doe raise last year will eat out of my hand now because I spend tons of time in the pen all year long, especially after weaning. Then they look for me to come and put treats in the trough and they gradually get tamer and tamer.
As for pasturized milk, yes there is risk with unpasturized, but the pasturizing process takes out all of the things that makes using natural, goat or cow, milk so great. I think if you are going to use pasturized milk, you need to ad probiotics and mineral supplements to make up for what was removed during pasturization. I use only unpasturized goat milk, and have had great success with it. My supplier runs a very clean farm and her goats are current on all vaccinations, so the passive immunities are in the milk for the fawns. I know the vet she uses, so I am confident her herd is clean and healthy. I am lucky in that sense, so if you don't feel you have that confidence in your fresh milk supplier, I wouldn't risk it, either. But I would add supplements to make up the difference. Whole milk from the grocery store (is that what you call red cap?) doesn't have half the butter fat content that unpasturized goat milk does, and has none of the good bugs and bacterias that establish pH and good gut function.
Just my $.02 - good luck to everyone this fawning season!