Welcome to FT, LMC!
Uh, since when does making a hotel booking always require prepayment? Hotels have lots of rates, and typically only a few are prepaid and/or non-cancelable.
For Y19,000 a night you could probably find a very respectable hotel room at a place such as the Keio Plaza or at Laplap's favorite, one of the Prince hotels in Shinagawa (I forget which one). And even in this economic downturn, no, you could not get the Peninsula at anything close to that price.
Most of these hotels do have non-smoking rooms on offer.