I have successfully hunted sika deer on private and state/public land, and let me tell you it isnt an easy hunt by any stretch of the imagination.
Between the hike/slog in (while not getting lost or going over the tops of your hip/chest waders), finding a decent tree near travel corridors (sometimes its literally one tree on a small island), getting mauled by mosquitoes (they laugh at thermocells, bring two minimum), having a shot opportunity at a very small animal in thick vegetation, blood tracking an animal in a water environment (while blood tracking I literally stepped on my first sika that submerged after it passed, lost blood, came back to the last blood, and my headlamp picked up the eye glint under the water), etc.
When it comes together, their is nothing sweeter than fresh sika meat. But you will earn every bite, and at points it seems like the mosquitoes took more from you than the meat you take from a sika. To give you an idea on size, my first two sika hinds weighed in at 27 and 36 lbs dressed,
I would go with archery tackle if you plan on public ground, the muzzleloader and firearms seasons are madness.
I have heard very good things from hunters that have gone with Whistling Creek Outfitters.
In my opinion, an old mature 6 point Sika Stag is one of the hardest animals to kill in the US.