Contact Director of Nursing via LinkedIn?

[wavesandsand]

I am looking to shadow a nurse and got the 3 names of the Director of Nursings at the major hospital in my area. However, upon calling the operator for that hospital, she told me that the information for 2 out of 3 of those DON's were not listed. I contacted the one DON who had her information posted and left a voicemail. I was able to find the other 2 on LinkedIn, and was wondering if it is acceptable to contact them via LinkedIn to inquire about shadowing in their particular departments. I am extremely interested in shadowing on trauma, med-surg, and ICU, which are the floors these two otherwise unreachable DON's are in charge of. Or, would it be better to wait to hear back from that one DON, and get in touch with them once in the hospital.. Advice?