For Friday night, will your hotel have an open bar that serves snacks? That might be the easiest solution for you. For example, I know that the Imperial has at least one bar (Old Imperial Bar on the second floor of the main building) that's open until at least midnight and has a menu of hot and cold sandwiches, among other things, although I don't know what time is the last order for food. The piano bar in the lobby seems to be open even later, but their food seems to be cakes and other fancy pastries. There's also a bar on the top floor which seems to serve F&B late, sometimes with live entertainment.

Another possibility is room service, which probably isn't your first choice. The Conrad should have a dinner menu until 11 or 12 and then all night snacks. Many hotels in Japan just impose the standard service charge and tax on room service without an additional delivery fee, so it can make sense even to ask for something small from room service, possibly to combine with stuff from your minibar.

If you want a standard cold Japanese box meal, they're sold all over, including in 7-11s and other convenience store chains, as well as in department stores (will be closed) and train stations.

Will a meal be served on your flight?

Have you contacted your hotel's concierge to ask for suggestions?