Washing silk a few times usually causes no problems at all. I have many silk shirts that I wash with my regular clothes. However, you need to realize a few things. (1) The silk will rip/tear sooner if you wash it. Basically instead of a normal shirt lasting 5 years with normal wear and tear, the silk shirt will get you 2-3 years with normal wear and tear. (2) Silk will lose its silky feel after 10 or so washes. It will start to feel more like hotel sheets than silk. What I do is wear the shirt 5-6 times between washings (unless I sweated in it).
If you are ok with those two drawbacks, then 99% of the time, you will be fine just washing it like a normal shirt. Heck you can even use detergent, warm water, and a dryer. Sure hand washing will maybe get you a few more washes, but nothing dramatic.