Cyclocross Newb Question

Last year, I did the Le Petit Train du Nord bike path, which runs 100 km north/south in the Laurentians in Quebec. Half is paved, half is not. I did it on my hybrid, but this year would love to do it on a lighter bike like my road bike, but the tires are the issue. I have a Giant Avail, last year's model. Any suggestions about changing the tires to be able to handle the gravel (which is not deep gravel, by the way) and not slow me down to much when I hit the pavement?

My husband has a Giant TCR, and he wants to do the path within this month, but I am not sure he CAN switch his tires, might be too tight. Is this his excuse to buy a cyclocross? He saw a sweet Argon 18 the last time we were doing that trail.

Not sure if there would be enough clearance...that's typically the issue. I really don't know though. Anyone?