Can i play my Xbox 360 minecraft worlds on Xbox One if I don't have my 360 hard drive?

The Xbox Xbox One doesn't use the 360's hard drive at all.

You can upload minecraft worlds to the cloud via the menu and download them on the other console.

You can upload your worlds to the cloud, then download it on an Xbox One. Otherwise, you're going to have to use your hard drive. Remember that the Xboxes except for the first one support backwards compatibility, so the Xbox One can load Xbox 360 data.

The only way to transfer worlds from the 360 to the One is by uploading them to the cloud on the 360, and loading them from there on the Xbox One. There's nothing that lets you read a 360 hard drive directly on the Xbox One