The delivery companies at Narita Airport will store luggage. It doesn't mention any upper limit. If you decide to go for that option, I'd visit the counters at Narita before you go to Hakuba and speak with them about what you're trying to do.
Charges may be rather steep for four weeks:
(Guidance is roughly 500yen per day to store a suitcase).
http://www.narita-airport.jp/jp/guid...st/svc_06.html
A better plan might be to set something up with a good hotel in Tokyo (or near the airport) - somewhere that you can spend the last night before departing - and find out if they can offer storage facility to hold your luggage for the four weeks before your check in.
Somewhere like the Imperial is likely to find a way to help you, I think. For a week or less, I'm sure it would be free of charge. For a month... well, give them a call and see what they say. (And please post the results here for everyone's benefit).