Is there a way I can power this circuit without a +- 15V power supply?
If you can find a 10VAC mains powered transformer, then you can make a simple power supply like this: 







simulate this circuit &ndash; Schematic created using CircuitLab

Failing that, two 12VDC-output switching adapters will do a fine job, at the cost of some convenience (two plugs have to be put in the wall). Put a diode (eg. 1N4004) across the output of each adapter (reverse biased) so that if just one is plugged in the other one does not see much reverse voltage at the output. 

The power supply voltage for your amplifier is not critical, a bit lower does no harm other than lowering the maximum power output (for a given speaker) a bit.

Laptop supplies may not work because some of them have the minus lead common with earth, so connecting them as required will short the outputs.