Hi Travellyn -
A look at a map will help you visualize those choices on the Rigi.
The cable car (Luftseilbahn, LSB) down from Kaltbad to Weggis has its bottom station a few hundred meters above the Schiffstation (Ship dock)
In the past, the only bus service from the Talstation was a bus to take children from up on the mountain to school in the morning and back in the afternoon, via the cable car. That seems to show up on some timetable schedules as "KB9" which I believe may stand for Kinder Bus ( children bus) #9. It has an infrequent schedule, as far as I can tell.
So, you generally have to walk that short stretch. 10 -15 minutes, downhill all the way.
However, the LSB is usually shut down for annual maintenance in late April.
Check the time table (linked by Annika in her first post) , using Rigi Kaltbad as the beginning station, and Weggis, Seilbahn and also, Weggis, Schiffstation as the end station. I did on March 20 and April 20 chosen as random dates, and the LSB is operating on March 20, but not operating on April 20,.2016.
So, you will probably not be able to use that route, since you will be there in late April. Check the time table for your preferred date.
If you did use it on another date, you , indeed could ride a boat back to Luzern, covering much the same route as the boat to Vitznau. There is also bus service along the lake shore to Brunnen and the Küssnacht-am-Rigi train station. It also connects at Vitznau.
The train ride down to Arth-Goldau is a nice ride, but is less scenic than the ride to/from Vitznau.
The bottom station is about 200 meters from the main rail station at Arth Goldau, and is awkward with heavy luggage ( stairs) as i recall.
Rigi is not such a high mountain, so the snow may be gone in late April. I tried to find annual temperature records on the internet, but for some reason, i could not find them for the Rigi. Altitude is important.
Perhaps Arno or Annika can suggest another web site for average weather on the Rigi in late April.