One Dangerous Zombie only activates in-game if you select 'Once Again' after loading a save file. I believe a requirement, additionally, is that the save has to have two clears as a single character or a clear as both jill and chris logged on it.

If you select 'New Game' without loading a save prior, One Dangerous Zombie will not be active.

To unlock One Dangerous Zombie you'll have to clear the game as Jill and Chris ("Once Again") on normal or higher difficulty (Furry wasn't sure about that, so I cleared it up ^^). As long as you prevent this you should be safe. Personally I would keep two seperate save files (one for each character) just to be sure or, as Furry mentioned, just start a new game without loading a file (depends on the category you wanna run).

if your running any% or best ending (100%) you dont need a save file once you beat it under one of them 2 categories create a new save file and you should be good

I used to run it with dangerous zombie because I didn't have a ng+ file without it as well, but in a speedrun and especially with Jill you won't come across him often enough to be a problem. He hits hard but I personally found him easier to dodge than a normal zombie