Off-season Uffizi strategy?
 

I'll be in Florence for 4 days in December, and I'm trying to figure out the best way to see the Uffizi (and other sites that offer reservations).

If all goes to schedule, I'll arrive around 1 pm on Saturday. The Sunday I'm there will be the free entrance day, so I don't want to go then. It is closed on Monday. I am in town all day on Tuesday, and I can make a reservation for then if I need to.

Is it unrealistic to think that I'd be able to walk in without a reservation on Saturday afternoon? (I say without a reservation because I fly into Pisa in the morning, but I'm reluctant to book anything in case of flight disruptions.)

Long story short: Will crowds still be significant enough in early December that i should make the reservations and commit to visiting top sites ahead of time?