According to the publication Welding of Stainless Steels and Other Joining Methods, which a product of the Nickel Development Institute (NiDI) and the American Iron and Steel Institute (AISI), "Carbide precipitation, for instance, will not occur during laser welding because of the high speed and low heat input".
Based on your question, I would say that cooling rate is a secondary variable to consider. You should probably be addressing the speed at which you are welding, and the amount of heat being generated in the weld metal during the process. Can you adjust weld parameters (beam power, beam diameter, etc.) to lower the heat input into the joint?
The next thing to consider is whether or not TiCN formation is really the problem. Slow cooling of ferritic steels, including stainless steels, through the temperature range of 565-400 C (1050-750 F), produces brittleness in the steel (known as 475 C embrittlement). This embrittlement is usually associated with ferrite grain boundary embrittlement by P, ans since TiCN will also be along the grain boundary, you may be experiencing this phenomenon. Ideas to consider for reducing this tendency include:
1. more aggressive cooling rate - forced air, water quenching (spray), etc.
2. Specify a lower P and C content - maybe limit P to 0.015 (instead of 0.045 max), and limit C content to 0.04 instead of 0.08.
3. Shield the weld metal from the atmosphere to limit O & N uptake in the weld.