Young milksnakes usually have great feeding responses so you should be able to feed f/t food items in the future without problems. Make sure it's nice and warm, jiggle it a little bit a couple of inches from it's head and it should get snapped up quickly.
I too really don't enjoy feeding live prey to my snakes, I've had to do it in the past for problem feeders but thankfully managed to get them all swithched over to p/k or f/t food. The worst one in my collection was one of my first corns who would for the first year of her life only eat live pinkies and fuzzies. It was terrible for me to watch as she wouldn't constrict them before eating, she would just swallow them alive and very often from the backside first. On more than one occasion, the little fuzzy was still squeaking after being completely swallowed! That is pretty sad I can tell you, to see the "bump" still moving and squeaking as it's going down...
In the future, I would let your snake manage with it's food item on it's own. It is extremely rare that your snake could choke on it's meal, it will spit it out if it is too big. It may seem like your snake was having a hard time but I would guess that it was just the usual contorsions of a young snake. I have noticed that very young snakes will go through quite an aerobic exercise when eating their first meals. My theory is that the instinct is telling them what to do but since it's their first times they are clumsy and take longer to do the job. After a few meals, they get much better and faster at "making the kill" and eating. All my hatchlings and very young snakes went through such a period.
Keeper of 5 snakes, leopard geckos, 1 green iguana, 20+ tarantulas, 2 dogs & a bunch of rats!