Is it OK to use an AC power supply with output voltage lower than specified on the original power supply to recharge a cordless tool?
That may work, or it may fry your power adapter and/or tool depending on the design of the internal charging circuit.  Your original charger supplied 2 Watts (8V * 0.25A), and your proposed replacement is only capable of delivering 1.8 W (6V * 0.3A).  If your charger pulls more current to compensate for the lower voltage (which is likely, assuming it works at all), then most likely your power supply will either blow a fuse or overheat and melt.  

One solution that might work for you if you're willing to do a little electronics work is a 9VAC adapter (which are cheap and common as dirt), plus a power resistor to drop that down to 8V.  Here's one that can output a full 1A for less than $5.  Since you know your device will be drawing about 250mA, and you want to drop 1V across the resistor, we can select a value with Ohm's law: 1V = 0.25A * R; R = 4 Ohms.  That resistor will dissipate (0.25A)^2 * 4Ohm = 0.25W, so anything 1/2W or bigger will be fine.  This would be one example of a suitable resistor.

EDIT: Another option, albeit slightly expensive, is an 8/16/24V Doorbell Transformer.  It has the right voltage and more than enough current.