I would apply it to just the piece and do it in stages.
1st time try try it for just under the recommended time and go from there.
Don't judge the result until its fully dry.
It really shouldn't matter if you get a bit on your natural hair and remember, this product washes out, so if it goes too dark, a good wash & rinse will start to lighten it again.

Do you have any of your piece left? You cut down a topper, so you could test it on the spare hair.