The use of fuses in small electronics projects
To answer your question, yes, those 1 Amp 250 Volt fuse will work fine in small projects, as the Voltage is a maximum. A 1 Amp 250V fast fuse should blow even at lower voltages. The important number here would be the Current rating.

For example, my multimeter has a 500 mA 250 Volt fast fuse, with a recommended/listed max current measuring of 200 mA. It has blown when I shorted out a 5V 1 Amp (USB) supply, and a 12V 750 mA supply by mistake.

You can test this with a spare fuse, and a resistor. Take your 9V supply and a 100 ohm resistor. At roughly 90 mA, the fuse won't blow. Short the fuse out, and it should.