The RadioShack wallwart you referenced is a dc supply, as the specs clearly indicate (read down), and its description as a switching regulator generally indicates that its a dc supply.
Your 12vac supply might work, might not. With a minimal load (300ma) the regulation of a 8va transformer should bring the voltage up substantially, 10-30%. It depends whether your line voltage runs high or low (mine typically runs 124vac), and if that voltage, after rectification, is regulated and how much voltage headroom is required for regulation.
Ideally, measure the 12vac warts output with a multimeter. I wouldn't think (but certainly am not guaranteeing) that even if the voltage is too low that it would harm your crossover.