You can use the Henry... like with any tube feed, the instructors should let you load an extra round, and then instead of the mag change, just break position, eject the extra round, and continue. You would greatly benefit from a rear aperture sight on it.
I would bring the AK too, even if you don't shoot the whole event with it. If for no other reason than to get a good zero with it (remember to bring a hammer and drift for that front sight and a front sight tool, if you have one), and to see how you do on the AQT with it. If it is your main center fire right now, you should be familiar with how to shoot it "Rifleman style."
The ideal rifle for the course is a mag fed semi auto with click-adjustable aperture sights and a GI web sling, but like the website says, you can bring any safe rifle and we will show you how to be a better shooter with it.