Technical:
1) Excessive capacitors for the 10cm lasers, C3 is enough.
2) Unusual tech, fire control and laser wavelength seem quite a bit ahead of the rest. Your weaponry matches that well; normally 15cm lasers dominate others, here your choices are equally valid. I'd normally prefer to match weapon and fire control tracking speed (10000km/s fire control), but that's not critical as most ships will be slower and your weaponry isn't focused on missile defence.
3) Conspicuous maintenance lives. Fine if they're explicitly designed to receive no overhauls/maintenance ever, excessive otherwise.
4) Thin shields over thin armour. What's the intention?
This looks ok if expectation is that they'll never receive damage (you have the weapon range for that, but the cruisers may not be able to maintain the range vs. fast enemies) with very slight precautions if that turns to be incorrect. Light shielding to avoid any damage whatsoever from an occasional hit at extreme range, light armour as a buffer if things go against plan.
I might beef up shields for the cruiser (seemingly designed to fight at extreme range where battles will be lengthy, giving it ample time to recharge) and armour for the Corvette (to have it maintain respectable speed in nebula systems).
5) Propulsion plants look fine; personally I prefer larger low-power engines but yours are still reasonable.
Doctrinal:
6) Your ships are excellent long-range beam platforms, with a nifty option to defend themselves in a brawl with microwaves. They can't defend adequately against missiles, they are on the fragile side, the cruiser can't force an engagement because of its lacklustre speed. Because of its limitations, it can't really do standalone cruiser duties, but with the right support it should be able to fill its niche competently.
7) Having both range and speed will allow flawless victories in beam combat. I'd consider something with the speed of the corvette and the range and electronic warfare suite of the cruiser, even if that cuts considerably into firepower.
You will need some point defence capability, whether on these ships or dedicated escorts. Your tech makes 10cm railguns attractive because of your very high base tracking speed.