What dimensions of AA batteries will fit Shure products?
For AA size, IEC 60086-2 LR6 and ANSI C18.1M 15A are the preferred standards. These specify a diameter range of 13.5 - 14.5mm (.531-.571"); the overall length is not problematic, typically, since Shure commonly employs a coil spring at the flat (usually negative polarity) end, and it compresses to accommodate length variations. On products, Shure uses a compliant contact at the positive end, so there's additional length compliance as a result.
Present (August 2015) handheld transmitters can take AA cells of this diameter:
UR2: 14.78mm (.574") nominal
BLX2: 14.78mm (.570") nominal
ULXD2 / QLXD2: 14.38mm (.566") nominal
Please note, ULXD2 / QLXD2 (and ULXD1 / QLXD1) can also accommodate the Shure SB900 Li battery pack
For present (August 2015) body pack transmitters, there isn't as well-defined information. The suggestion for AA cell diameter to fit into UR1, BLX1 and ULXD1 / QLXD1 is to be below, or just at, nominal of the specification (13.5-14.0mm).
Forthcoming handheld mics and body packs are being designed to accommodate AA cells per the ISO and ANSI standards.