The N9 boots if you connect it to a power source, so you can carry a very small power bank with you and use it to boot the N9.

For shutdown you can just use the terminal or use the handy application PowerControl which gives you a icon that offers you the choice to reboot or shutdown.

You could try opening your N9 and repairing the button. But as the power button requires a nearly complete disassembly I would not recommend it if you don't have experience.