Choosing the right transformer to replace batteries?
160mA at 6V is about 1W that would be easily suffucuent for a fairly bright LED path light.

If you're not equipped to measure the current consumption of the lights 
maybe go for a 2A 6V supply that should be plenty if you estimate is in the right ballpark.

You could probably even use a 5V 2A "phone charger" as battery powered devices are usually designed to operate from as low as 1.1V per cell so 5V should be plenty.