Whisking egg whites with a fork is doable but it's harder on your hands than using a regular whisk to Whisk the egg whites.
To whisk egg white using a fork you need to use two forks to create a whisk and then whisk like you normally would.
Whisking with a single fork won't do much good as you need both the forks to form a whisk to do the whisking properly.
I've done whisking with forks but am so glad I bought a whisk as my hands hurts less than when using the forks.
If you have no whisk then 2 forks will work to whisk the egg whites or anything else but I would recommend buying a cheap hand whisk for better results.