I think you can also buy cups of ice at a combini if you need some while away from your hotel. It is meant to make iced coffee, I believe? I often carry around sufficient bottled water in hot and humid weather but reduce the load a bit in Japan since I've even seen working vending machines in the middle of the sparsely populated deep countryside. I'm not always near a combini but a vending machine is usually nearby. Just be aware that trash cans are rare. I'd bring an insulated bottle if only to dump the ice/drink (with leftover hotel ice) into and recycle the disposable* cup/bottle at the combini trash area before leaving. City vending machines will usually have a bottle recycle bin with precise cutouts and no trash can.

* Clarification: Purchase bottled drink and/or ice, decant into your insulated bottle at combini, and recycle now emptied plastic drink bottle at combini where there are trash facilities. If it is a bottle from a vending machine, there is usually a recycling area right next to the machine just for bottles. This will help keep your drinks cool for longer without carrying around excess water weight or having to pack trash back to your hotel. Abundant vending machines with cold bottled drinks and scarce public trash facilities are some of those "Japan does it differently" things worth knowing for new visitors arriving in summer.