Really nice idea, very creative and works great with the minimalistic art. I had some trouble with the controls at first, firing with the mouse might feel better. The jump also didn't feel high enough to navigate through some of the new platforms, especially with the aliens coming to get you. Maybe a small tutorial at the beginning can help with figuring out the controls and the shop, as well as being able to move around your new ship in the shop menu.
Overall I think the idea is great though and has potential!