4 years of med/surg seems a bit much... usually they're happy with one (which I had, although I later wished I had had more

). Anyway, it does sound like you are well prepared for a career as a dialysis nurse - supportive, understanding nephrologists are a great plus for you. Also, they know your background and know that they can't except you to know certain things (which you would have learned in med/surg) yet; but it will come.
My hospital acute unit (they once had a chronic unit years ago, but that was bought by a large national company) took a chance on a new grad 7 years ago, and she's one of the best nurses they have! So don't let that hold you back or even question your ability to become a competent dialysis nurse. Also, you're "mature", which also helps a lot (so was she, 40 when she started).
I do hope that you also have good fellow RNs and other staff; don't hesitate to ask any and all questions you have! Especially as a new grad, you may have questions about assessment findings; ask them to double check those adventitious lung sounds if you're not sure! You should have a preceptor/mentor, who should be available to you even beyond your initial training period. Believe me, you will still be very green at that time (and they know it), but it will all fall into place.
Again, all the very best,
DeLana