The laser does indeed have recoil; however, the momentum of the particles p=h/lambda isn't very much (h is a very small number). The laser would be slowed a very small fraction.

Do blasters have recoil?

Blasters in Star Wars do have recoil. They operate on the same principles as firearms in real life. A projectile is being fired from a barrel with high velocity. ... If they fire all of their blasters in one high intensity volley, the blaster rifle is going straight in the air.

Why do laser weapons have recoil fallout?

Why do laser guns have recoil? ... As it passes through it scrapes against the lens as it changes from light to solid which could be what causes the recoil.