Depending on the hotel involved, they may charge the card you've given for a guarantee at any of a number of times.
1) When you make the booking, or shortly afterwards. In this case you'd normally be told this was going to occur when you made the booking, but given you're going through a 3rd party it's still possible even if you were not told.
2) Shortly before your stay - normally around the time the free cancellation expires (maybe a day before arrival, maybe a few days before)
3) Only once you actually check-in, at which point you'll be able to provide a different card.
In a generic sense, there's no way of knowing which of these options they will take. On my stays in Japan I've had both of 2 and 3 happen depending on the hotel.
If they are unable to charge the card at the time, most hotels will make an attempt to contact you to obtain a new card - however this could be difficult given you have booked via a 3rd party. If they are unable to contact you then they may cancel your reservation - especially if the hotel is (near) full for the time of the booking.