Will a CR2477 coin cell battery make a nichrome wire glow?
Your first step should be to read the datasheet of a CR2477.

Here is one, this is for the one from Panasonic, CR2477 cells can be made by other manufacturers also but the numbers in the datasheet will be in the same ballpark.

Now look on page 14. There are some graphs but they all list currents below 1 mA, that is 0.001 A. So 1000x less than what you need for your wire. The fact that no data is plotted for currents above 1 mA suggests that it is not intended to be used at much higher currents. 10 mA maybe for a minute but 1 A, forget it !

The CR2477 will probably not explode or whatever since it has a very high internal resistance which limits the current. It will just get slightly warm until its energy is depleted.

This CR2477 is a Lithium button cell and these are designed to provide a small amount of power over a long period of time.

What you want is much more than such a cell can even hope to deliver. You would need a couple of hundred of them in parallel to make your nichrome wire glow even dimly.

Conclusion: No, a CR2477 is not going to work.

Some 9 V batteries might be able to deliver the power you need (if you stick to the alkaline version) but only when they're very fresh. So you'd have to change the battery often.

You should really consider using 4 AA batteries in series for this kind of application.