Question about a sampler

An email from T.S. asked the following:

Pardon my ignorance regarding looping and the related technology as I am new to this realm of music production. There is a very specific application that I have in mind for live performances with other musicians, and wonder if a set of products exists to accomplish the objective. Here is a description:

1.         A hardware device that can import several pre-recorded one to four measure bass lines and percussion loops. Each loop will be named and targeted for a specific song to be performed live.

2.         The named loops can be “dialed up” on stage as needed for each song to be performed.

3.         A large button-like device connected to the hardware device that can be hit by hand (not foot) in time with the other musicians to trigger the one to four measure loops.

4.         The one to four measure loops will play ONLY ONE TIME through when triggered and then stop until triggered again with a subsequent hit to the button. This will allow the on-stage musician triggering the loops to play the loop on demand, so to speak, when needed and in time with the other musicians on stage.

Is such a hardware and software configuration possible? If so, can you provide me information on the set up? Many thanks.

I would like to share the response for the benefit of others and in case there are more ideas out there:

Also, here is the product from the video: