How to approach Managers?

Before you say don't, hear my story. I will abbreviate to keep it short.

My hospital is making a float team to keep from using registrty/agency nurses. They hired a bunch of new grad RNs as CNAs to transition to RNs via a new grad residency. They were only going to give people a few units to float too.

So far its been disorganized to say the least and the story is always changing. I have been very concerned about getting an RN position at all. I think they hired way to many new grads. They sent us an email stating if we want to go talk to any unit manager about a position we can and that every non ICU unit is hiring.

I am planning to go to all the managers next Monday with my resume. Just not sure what to say. I am not very good at the office professional angle (if that makes sense).

I was thinking of something like "Hello my name is _____ I am a CNA new grad RN with the float team and I wanted to inquire about any position you have available on your unit." And kind of go from there. I plan to go to the units I know we'll and have worked on a lot first. I plan to have a reason for why I want to work there and then sell myself. I was a Navy Corpsman, an lvn with 12 years experience including IV certification and experience hanging blood, meds and doing IV pushes (something I could do as an LPN in another state but that LVNs here can't do).

Any advice on what to say? Should I bring any other than a resume?