Changing a plug on my Henry vac?

My henry has recently died due to over-zealous tugging around the plug. I wanted to change the plug but when I cut the wire back, I found only a blue wire and a brown wire inside the black cable...

In the new plug i bought there is space for three wires to be attached, I am assuming one is the ground wire which is pretty important, no?

I am very clueless about all of this and would lika any advise on what to next, in the simplest layman terms possible please!

Thank you so much

Dee :)