The closest idea that comes close to what you may be thinking would be doing a Working Holiday Visa in Japan. You can do a Working Holiday Visa if you belong to one of these countries:
- Austrailia
- Canada
- France
- Germany
- Ireland
- South Korea
- New Zealand
- Hong Kong
- United Kingdom

Considering what you want to do (i.e travelling by foot and using tents), I don't think this will be possible (you could walk, but using tents would be a no-no id imagine). I don't know about the whole cash in hand thing, I think if your WHV gets processed by Immigration it may be possible depending on the work involved. The whole point of the WHV is to get work to supplement your travelling.

There are requirements and restrictions for obtaining the WHV such as your age. You also have to submit to your Japanese Consultate your reasons for going and also your travel itinary. You need to have sufficient money in your bank account to support yourself until you find work. There are usually limits on the type of employment taken, or the length of time the traveller can be employed for.

You can find out more information from your countries Japanese Consultate, but if you don't belong to one of the countries that partipates in it then there is really no point in finding out anyway.