Do I really need Ramps 1.4 for laser engraver
Ramps 1.4 is one of the proof of concept standards for 3D printer systems. It is a motherboard mostly runs Marlin firmware on it. I advice to to take a look at the firmware if you didn't yet. It is also supporting many motherboards, hardware.

When you open the configuration.h file in the firmware and search for this definition #define MOTHERBOARD you will be seeing many options available.

After all, the firmware is the key factor. It contains many engineering solutions in it. So, you shouldn't re-invent the wheel.
All you have to do is to adapt it with some tweaks as per your design specifications.

But, I would worry more about your motherboard (Arduino Uno)
if your design is relatively simple, using less memory and IO pins, it may be just fine. I would consider Mega 2560 instead If I were you.

Good luck with your project.