<<"I have to catch atleast a 4:05 PM train so that by 6 PM I will reach Interlaken and then move to Wengen in good light as well and reach before 7.30 PM. Because I suppose it would be dark in the mountains well before sunset..Not sure just my guess..So at least half an hour before I wanted to reach..">>
This website gives more information than the site that I linked before:
This one gives a much better sense of daylight hours, but Spiez is the closest town that it shows:
Civil twilight in Spiez on September 17th is at 2007. Sunset is at 1936
Down in the Lauterbrunnen Valley, it may be dark sooner...the mountains block the sun. However, Wengen is half way up the mountainside, facing south and west. It will have sunlight later than the valley. probably somewhat comparable to Spiez, although perhaps not quit as late. The sun can be visible longer when you are up in the mountains, provided that other mountains don't block its light. If you have a cloudy day, of course, that will mean an earlier twilight.
If you catch the 1605 train from Luzern, you will be in Wengen at 1851........45 minutes before sunset.
If you catch the 1705 train, you'll indeed arrive at 1951, 15 minutes after sunset, but will have twilight for about 15 minutes after you arrive at Wengen.
Is your hotel close to the station? If not, they'll generally send a small electric cart to pick up you and your luggage if you telephone when you are at the station. Either way, you won't get lost, but, indeed, you'll want to catch the 1605 to have a safety margin. If you are concerned, you might check before hand if the hotel will pick you up.
Going to the Rigi -
The earliest boat from Luzern to Vitznau with good connections to Rigi Kulm is the 0812, arriving Rigi Kulm at 0947. The next is at 0912, arriving 1047. Etc.
Returning to Luzern -
On your planned return via the cableway from Rigi Kaltbad to Weggis, you could leave Rigi Kulm as late as 1400.
The only problem with that is that you have a 15 minute connection from the Luftseilbahn (LSB, cableway) at Weggis to the Schiffstation, and it is a 15 minute walk. Downhill, but no time to spare. I assume you'll leave your luggage at the station in Luzern.....
If instead of using the cableway via Weggis, you stay on the cograil train and continue back down the mountain to Vitznau, you'll catch the same boat to Luzern, which stops at Vitznau a few minutes earlier than at Weggis, with a less than 100 meter walk to the boat and 9 minutes to do it.
So, to be very safe, if you choose to go back via the Weggis LSB, I'd take the 1300 cograil train to Kaltbad. You will not have to rush to get the boat.
That is a very nice scenic ride on the cableway. I use it regularly when I stay at Rigi Kaltbad.
The walk I mentioned previously would take as little as one hour or as much a little less than a couple of hours. So, I'd not try it unless you took the earliest boat (0812) to Vitznau, arriving at Rigi Kulm at 0947, looked around for 15 minutes, and started your walk down hill as far as Rigi Staffel Höhe and turned out toward Chänzeli quickly. Or, you might squeeze it in if you caught the next (hourly) train down to Staffel Höhe, and then walked via Chänzeli. I could do it, because i know the way well. If I were you, I'd not try either one, if you want to surely catch the 1605 from Luzern to Wengen. If you are a "speed walker" and check out the route carefully on the maps before you try, you could do it, but you would have to go quickly . I'd not try it for the first time without more leeway in your schedule. I like to stop and take photographs. Those judgements are very personal.
Return via Arth- Goldau?
An alternative is to return from Rigi Kulm to Luzern via Arth Goldau.
In that case, you would catch the 1404 down the mountain to Arth-Goldau, walk 268 meters to the main line train platform and catch a 1514 to Luzern, arriving at 1541.
There are two problems with that idea -
1.- You only have 7 minutes for the connection at Arth-Goldau, and it is tight, because you have to go down a batch of of stairs at the bottom station (Talstation, valley station) of the Rigibahn , then hurry 268 meters to the main platform. So, you might want to catch the 1304 down from Rigi Kulm.
2.-It is not a very scenic route.
The surest route with no rushed walking for an approximately 1400 return from Rigi Kulm is to go back via Vitznau. Otherwise, you will have a safety margin of about one hour if you go on the other routes but leave Rigi Kulm at about 1300. And if you decide to leave Rigi Kulm earlier, the trains down run once per hour.
You can think about the schedules and decide if you want to spend 1, 2, or 3 hours at Rigi Kulm.
You can leave Luzern at 0912 instead of 0812, and you can leave Rigi Kulm at different times.
If you do have spare time when you get back to Luzern, you can walk along the river and around the old city easily...it is less than 10 minutes from the main station.