How to delete my hand in my video.

As others suggested, using a green glove could work. But make sure the puppet you're filming doesn’t have any green on it, or it’ll be difficult to separate the glove from the puppet during keying. Also, keep in mind that removing the glove will leave a hole in your footage—so it’s important to shoot a clean plate (an empty version of the exact same frame without your hand) that you can use to fill in that gap. This will make the post-process much smoother and more convincing.

When I initially read this I initially thought about a green glove and Ultra Key tool.

Maybe you could also use the mask tool to mask around the hand and use the suitable filler layer above to blend in with the hand area.

This depends on what the puppet /hand shot looks like. A hypothetical example might be a rabbit and then you use fur image details in the mask / feathered to look part of the original shot ? 

Whatever they used with Kermit it was pure magic.

If you wear a green glove you might be able to use the Ultra Key effect to isolate the puppet, depending on the lighting and the colour of the stuffed animal.

In the 70s we found you could not green screen Kermit but chroma blue worked well.

Might need to use rotoscoping in After Effects

or make the puppet larger than your hand.