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Some browsers will rely partially on the stock browser so before you delete it I would freeze it and reboot then test out the browser you like to make sure it functions fully. If it does then it should be safe to fully uninstall the stock browser.

 

Don't take this the wrong way because I'm just genuinely curious, but I don't know why it would be worth removing? I can't imagine you would possibly gain any speed from this, the space it takes up is very minimal, and if your browser of choice crashes a certain page or gets a buggy update, etc, you have a quick backup browser already installed with no effort required to use.

I guess I'm looking at it kind of like the way I would never ever choose internet explorer to open a page up on my windows pc but I just accept that it's a built-in