The RS Swiss Guide book includes all the necessary info for Mt Pilatus, and the various modes for ascent and descent.
I agree, you don't need a tour , it's easy to do on your own.
If you have the Swiss Travel Pass, you may consider Mt Rigi, which is completely covered, along with Mt Stanserhorn. Mt Rigi includes the delightful hour boat ride to Vitnau , where you catch the cogwheel train to the summit. The efficient Swiss time the boat and train to connect smoothly. Altho I haven't done it, there is also a gondola on the opposite side, which takes you to Weggis to catch the boat. This option requires a little bit of walking. ( Or you can reverse the order .) For us, this was a half - day outing, as I think we took a boat a little after 9am, and returned to Lucerne after 1:00pm.
My Stanserhorn is a much shorter trip, and is a nice sunset outing. It took us a total of 45 minutes from the Lucerne train station to the summit, and included an open air gondola, which was really cool! There are an eating options at the summit. This is also completely covered by the Swiss Travel Pass.
Mt. Pilatus is only discounted by the various travel passes .
A poster here noted a Swiss Travel Pass sale starting April 15.
Have a great trip!