Transient spikes are bad, you're right there. You need to be careful with laser-diode drivers as they must be Current-regulated, so you set the current output of the driver, and it produces whatever voltage at the output which will cause that current to flow in the load. This unfortunately means that putting a large output capacitor over the outputs won't act to smooth spikes in current, but will actually contribute to them when the unit is powered on and off.
This is because Laser Diodes reduce in resistance as they warm up - which if fed with a voltage-regulated driver, will quickly increase the amount of current in the diode, warming it up and so on - thermal runaway, which can damage the LDs.
Most CNC laser engravers I've seen in the past use focusable modules already mounted in heat-sinks with drivers - i.e. you can get a module all put together if you like - and these are pretty affordable too from the usual Chinese suppliers (AliExpress/Banggood) etc. For a CNC engraver - you also need to consider how you modulate the laser - i.e. how you dim it, and turn it on and off rapidly enough to allow you to control it properly. Specifically designed laser modules will have additional inputs which modulate the laser diode - things you will need to consider also.
In general, I discourage you from using a driver not designed or specifically suited to driving powerful Laser Diodes to try and save a few euros. A good laser driver specifically designed for high power Blue diodes is the BlackBuck 8M - which has lots of options for modulation etc.
