Unfortunately, there is no safe method to remove Internet Explorer from Windows XP.
Internet Explorer is more than just a browser. It works as an underlying technology behind a number of internal Windows XP processes including updating, basic Windows functionality and more.
There are methods outlined on some other websites that appear to fully remove Internet Explorer and provide workarounds for the problems that removing it causes, but I don't recommend them. In my experience, removing IE causes too many problems to be worth it, even with the workarounds.
Even though removing Internet Explorer isn't a wise option, you most certainly can safely disable Internet Explorer and use your alternative browser as the one and only way to access the Internet on your Windows XP PC.