It is far more easier to remove the shelf from the wall than to take
apart a toilet tank just for the sake of leaving the shelf where it
is.
And yes, they sell replacement parts for that type of flapper. These
guys are pretty good.
http://www.plumbingpartsdepot.com/
They have all drawings and schematics online for a lot of toilets.
Chances are you can find the OEM part for your toilet.