I'd seriously suggest passing on Spooner Lake and hiking up to Martlett Lake. The trail starts in the same area as Spooner. It's the same trail as the famous mountain biking Flume Trail. It's about 5 miles up hill but the lake is full of Lahontan Cuts. They just opened it up to fishing a few years ago, before that the fish in there were used as brood stock to try and re-introduce the Lahontans into the Truckee. If you're fit enough you would do really well to bring a float tube up there. You will need a Nevada license to fish Spooner, Martlett or Hobart lakes. I've biked up there before and it beautiful!
I agree with Packrat. Take a bike and go enjoy Martlett. I've biked in there the last few years and done pretty well. Never caught a Cutt in there but I have caught some Brooks and Bows.
I've never fished Spooner so I can't offer much help on that. I have heard there are leeches in there and always taken a pass.