You should be able to recover them on your side yes, and then I would suggest saving them in multiple places as well as using a password manager plugin possibly.
Ideas for keeping keys -
I don’t know which one you have been signing in with, so I don’t know what is saved in your browser, but once you have them all (Master, Owner, Active, Posting and Memo)
Label which is which (and what you need them for)
Save them to a pdf (if you enter your master in the Steemit site, a pdf will actually now be offered to you).
Print multiple hard copies and keep them in safe locations
Save pdf on a thumb drive and keep it safe
Use a password manager for daily use. (Ex. LastPass, 1password or keychain.)
RE: Important Changes to Steemit.com and Wallet