I'm not sure which service you are using but if you are using Yamato (Takkyubin), Sagawa, or post office, you don't have to worry. I think Japanese delivery services are in highest standards. Especially Yamato's Takkyubin service is so exact about time.
Yes!! I always use this. The shinkansen do not have a lot of luggage storage space and tourists often look and feel clumsy hauling luggage. I've used the 'takuhaibin' service between Tokyo, Fukuoka, Matsumoto, Nagoya, Nozawa onsen, Osaka, Kyoto etc.... My luggage is always waiting for me the next day by the time I arrive at the hotel. They pick up at all the hotels I've ever stayed at so ask your front desk for pick up service. They can help you fill out delivery slip. You drop of luggage at front deck usually by 10am, and it will arrive at your destination the next day (so keep an over night small pack with you) I also have used Sagawa same day luggage delivery Tokyo 23 wards when changing hotels in the city and the luggages are usually there by 4pm check in time same day:) I also agree that Yamato 'kuroneko' and Sagawa are very reliable. My luggage has never been damaged and never had any items missing. The prices are very reasonable.