If you participated in any formal retirement savings plan (401, Roth, employer pension, annuity, Social Security) a copy of a recent statement should also satisfy a landlord that you are financially secure. When you call for a showing, let them know you will be able to provide these alternate documents since you are not currently an active employee.
I think a 401 statement showing several hundred K, will ease the concerns of any potential landlord or management company. Don't worry about a credit report. They will normally get that themselves to verify your declarations. If you work with a realtor or management company you will probably get by with just the single 'ping' on your credit rating.
Relax. Good luck!
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