I spent some time with the paper time table book.
Since your return to Zürich airport will be critical, and the boat schedule from Vitznau or from Weggis to Luzern will be the critical path for your return journey, if you go back down to Vitznau or take the cable way and walk to Weggis, that is waht I looked for.
In the Fall schedule, boats leave Vitznau for Luzern at 1449, 1549, 1649, 1749, 1811, and 1849. On weekdays only, 1911. Also on days4-6 (Thursday through Saturday, at 2011, which is tooo late to get you back to the airport, anyway.
In the Fall, They leave Weggis 16 minutes later ( same boat) at 1505, 1605, 1705. [no 1827...bypasses Weggis] and on workdays, (Monday through Friday), at 1926, but there is no late boat after the 1926 from Weggis.
You are concerned with the Winter schedule, on a Saturday (day 6 of the week).
Boats from Vitznau leave for Luzern at 1449, 1549, (1649 Sundays only) 1749 and 2011.
From Weggis- 1505, 1605, (no 1705), 1755 ( Monday through Friday) and 1805.
To arrive at Weggis for the 1805, you must leave Rigi Kaltbad at 1725 on the cable car ( LSB) and arrive at the valley station at 1735, then rush in the dark to the ship landing , taking a nominal 15 minutes, arriving at 1750, and catch the 1805, assuming that you do not get lost. I'd consider doing it in the daylight, or even in the dark if I had done it once before. Will you be jetlagged?
You might try to do it on an earlier run.
Then, you would have to work the timetable to see what goes down from Rigi Kulm on a Saturday early enough for you to catch the 1749 boat at Vitznau ( easy fast connection) or make the walk from the valley station of the LSB to the ships landing in Weggis and catch the 1805 boat to Luzern.
Trains from Rigi Kulm down to Vitznau all stop at Rigi Kaltbad. From the train station it is about a 3 minute walk to the LSB station...allow a little more in the dark.
Here are the options- in Winter-
Option 1- with multiple connections and no boat -
Depart Rigi-Kulm at 1600, via Rigi-Kaltbad -First ( same as Rigi Kaltbad) at 1613, to Vitznau at 1640. No boat at 1649 on a Saturday. Catch a bus to Küsssnacht am Rigi Bahnhof at 1652, arrive 1722, and get a train to the airport via Zürich leaving Küssnacht am Rigi at 1726 arriving at the airport at 1847 ( 2 hours before your flight) with changes at Arth Goldau ( 7 minutes connection...easy) and Zürich main station at 1828 with a 9 minute connection incoming and outbound on the main train platforms close to each other.
If you went via Weggis, you still have to walk to the ship landing to catch the same bus to Küssnacht am Rigi, thence to ZFH.
I'd do that , but I'd not recommend it to you ....in the dark.
Catch the 1749 boat from Vitznau or the 1805 from Weggis.
Take the 1700 down from RigiKulm to Vitznau at 1740.
or, get off at 1713 at Rigi-Kaltbad, walk three minutes to the cable car (LSB) , just miss the 1710 cable car and catch the 1740cable car from Rigi Kaltbad First to Weggis at 1750, and run very fast in the dark to catch the 1805 boat. I'd not try to do that myself.
I'd not recommend it for a first time visitor, and I'd strongly recommend against doing it if you will be jet-lagged ---but it is not impossible.
The Swiss are very helpful to travelers.
If I were doing that, I'd explain to the operator of the cable car what my situation is in English, and ask if he or she could ask the passengers if any of them could drive you to the boat landing. More than likely, he or she will know the regular passengers, and would be willing to ask for a ride in general anyway, in Swiss German....
If you catch the 1805 boat, (same boat that leaves Vitznau at 1749) you arrive at Luzern ship landing at 1841, catch the 1910 to Zurich main station at 1956, which continues with out change of train arriving at Zürich Flughafen at 2013.
Same results if you ride down to Vitznau arriving at 1740 and catch the same boat , departing Vitznau at 1749.
Thus, that is all theoretically possible.
If you want to go up by cograil, you can do the best trip - train to Luzern from ZFH at 1147 - you should be able to make that and stash your luggage in a locker , as long as you are not sitting at the back of the airplane, and you buy your tickets from a ticket machine., or a short line at the ticket counter.
It can be tight if you are not fast with those chores. I'd worry a bit. and, if you miss that 1147, the rest of the schedule gets messy....5 minutes on top of the rigi, for example.
Or, a complex route via multiple buses which stlll gets you to the Weggis ship landing 18 minutes before the UPHILL walk to the cable car at 1410. Don't try it if you are jet lagged
See attached screen grab.
Summary- there a lot of ways to do the routes that you desire, but they all involve tight timing at one point or another, or, only a few minutes at Rigi Kulm.
By backing off on the routing to take part of the trip on the less scenic route ...via Arth Goldau... you have more flexibility and some time up top..
How hard are you prepared to work at it, and can you use the complex contingency plans with multiple changes of buses, remembering that sunset is at about 1640?
I think the safest route which still allows the cable car is to go up from Weggis, in spite of the walk. Then , you can go down via Arth Goldauu for the fastest return to Zürich. and get the boat ride in, too.
Then, get up to the top at 1447, stay 1 hour and 5 minutes, catch the 1600 down to Rigi Kaltbad, and catch the 1805 boat with a long wait at the boat landing, or catch the bus as noted and go via Küssnacht am Rigi.
If you can make the 1147 train, it will help a lot.
If you leave out the cable car, life is a lot simpler.