I've had a good look on Google Maps and street view.
Is it possible to walk out of the airport? Maybe, yes. There seems to be footpaths alongside most of the roads you would need to walk, or a part of the road marked by a white line at the side, or at least a grass verge to walk along. Where you need to cross a road there are pedestrian crossing marked on the road. I even saw some people walking on street view.
Is it safe? Maybe, see Jan's answer.
Unfortunately, the biggest problem might be getting back into the airport. The terminal area is surrounded by a security fence. The footpaths go through the fence at various places, each with a gate and a guard. I don't know for sure, but you might need a specific ID to get through the gate, particularly if your are entering the secure area on foot. I suspect these gates are for airport workers, and a passport and a plane ticket won't cut it. You might get lucky and the guard will take note of you, promising to let you back in, but what will you do if you return a couple of hours later and the shift has changed?
Anyway, here is a route I think might be possible, starting from the hotel right outside terminal 2: https://www.google.com/maps/dir/35.7725914,140.386262/35.775505,firstname.lastname@example.org,140.366927,2880m/am=t/data=!3m2!1e3!4b1!4m2!4m1!3e2?hl=en
After about 800m you come to the security gate.
A similar route seems to be possible from Terminal 1, taking about 10 mins longer.
TBH, I think you will have a bigger problem at these security gates - with language and procedure - than getting a bus or train to somewhere. And I think there is a significant risk that you find yourself stuck outside the security cordon, or being led away for questioning.
Lastly, I too have had to hang around an airport for hours on end. I had a lengthy brunch and looked in all the shops, and out the windows at the planes going by - 6 hours just flew by. In your case, I would question the need to visit the park, on foot. It is a lengthy walk alongside roads, it is well past cherry blossom time and there seems to be little else to do there except watch the planes go by; and for that you can get a better view from the terminal observation decks.