Let me quote a paragraph from the page I referenced above:'A network of pleasant hiking trails covers the mountains and hills surrounding the lake, as well as the Aokigahara Jukai, lit. "Aokigahara tree ocean", an expansive forest south of the lake, famous for people getting lost.'
This would indicate that if you stay on the "pleasant hiking trails" you would stand a better chance of not getting lost. I suspect some of the people who 'get lost' there really want to 'get lost', because their intention is to end their lives. If that is not your intention (and I hope it is not), then go. It never hurts to take a gps device with you anywhere, so that you have an exact read on where you started in case there is any confusion about getting back to that place. But if you exercise some caution and follow the rules (and the paths), and don't succumb to doing any "exploring" and be sure to finish your hike well before dark, you have maximized your chances of not making trouble for the local search and rescue outfit (which I understand is tired of needing to find people who want an "adventure.")
Compasses should be okay too if you know how to utilize them and if they are calibrated for the region where you are (which is different in different areas around the world because of the magnetic poles not matching the geographic poles). As said in this thread several times, there isn't anything in the mountain/forest/lake area that should affect a compass, but legends like this sometimes have a kernel of truth--in this case, perhaps even people who had compasses didn't know everything they need to know to make the best use of them.
Personally, I would find looking at the Tree Field Ocean from several possible viewpoints outside it to be at least as impressive, maybe more, than getting inside it and seeing just the "trees" and not the "forest".
Probably most countries on earth offer locations where you can get disoriented and lost. I think if I just HAD to get disoriented, I'd rather do so somewhere where I would be sure I could read the maps and signs and speak with people I would be likely to run into.
Enjoy yourself but be careful.