Laser welding (especially pulsed welding) has propensity to form cracks in 316 SS. The main source of crack formation is the solidification mode. If the melt solidifies as primary austenite, the austenite phase has low solubility for impurities and rejects them; the impurities (sulphur and phosphorous) then form low melting phases with Fe and lead to cracking. 304 is much easier to laser weld since the melt has some ferrite content which has much greater solubility for impurities and avoids cracking.
A mixture of 304 and 316 should be free from cracking. In case your experiments do indicate some level of cracks, you can try biasing the laser spot towards 304.
Additionally, it is always good to keep the carbon content low by using the L grades.
Keep in mind that the acceptable range of 316 is right on the border line between Austenite solidfication and Austenite+Ferrite. So you may find that some batches of 316 crack and some dont. This has caused issues with one of my customers who qualified a part based on experiments on 316 but when they went into production, they found the parts were cracking.
Girish
http://www.welding-consultant.com