Hello There,
I live in Westford also and have tried several different swim lessons for my 7 year old boy. The best and most effective that I keep going back to is Pool School Plus in Harvard/Boxborough. You can find them on line (be careful to find the right one as "pool school" itself is a franchise business. Anyway, these folks are great with any level swimmer and I think they do Saturday lessons; not sure about private. But, they do have small swimmer to teacher ratios, especially for those who are new to swimming (like 4 to 1). You can also try the Westford Swim and Raquet Club or the Regency --I'm pretty sure they both have Saturday lessons, though I don't know much about them.
Good luck!
B.