The lack of service history will make a difference to the value. However whatever you choose to do the hybrid battery check is worth doing as it preserves the battery warranty.
Interestingly I am looking for a RX450h of similar age/spec to yours, so if you are thinking of selling privately let me know, I am a way away from you but travel (legitimately) with work to your area, and the private sale price should be more than Webuyanycar type prices.