<<"on 17-21 May 2018, and then will travel to Zermatt for any other 2 nights,">>
Alpenrose has posted a list of opening times for various transport services in the Jungfra region.
I'd link you to it, but forgot to bookmark it. ;-(
Most will open just after you leave.
Some trails ere groomed in the Winter for hiking....I believe that First<-> Bachalpsee is one. However, as the ski season finishes and the snow gets poor for skiing, many cableways shut for maintenance, opening sometime in late May or early June for hikers. The trails are no longer maintained in the interim, and you wait until warm and sunny weather has made them passable safely.
An easy one discussed in this forum recently that should be OK is Grütschalp to Mürren, which you could combine with a trip to Schilthorn.
I recall that the Schilthorn does its maintenance in the Fall. You can check their website, or:
It seems that you have the high Alps set as targets for your travels. Not to dissuade you, but to offer other options, you could consider lower altitudes.
In May, hikes at lower altitudes or in sunny regions are quite feasible. The following two are quite nice, show a lot of beautiful Switzerland, but are not good for seeing the famous sites that you have mentioned.
Spring will be well advanced at Luzern's altitude and in the surroundings:
( I prefer to use the German spelling - Luzern - because it is what you will see on all the signs for Luzern in the German-speaking regions where you will spend most of your time).
The Rhone Valley, especially the south-facing wall is dry ( rain shadow) and gets a lot of sun. There is a nice walk on that wall, maintained by the BLS railroad company. Some of it is the residue of the access facilities, including sections of roadbed for a narrow gauge supply train, used during construction.
That BLS rail line, which the trail parallels, is the southern approach ramp to/from the older upper Lötschberg tunnel; the northern approach ramp goes up from Spiez to/from Kandersteg.
So the trail is called by its German, name, thus- the BLS Südrampe Trail.
I mention those as examples of hikes at lower altitudes.
One in the Jungfrau region would be the easy almost level walk along the floor of the Lauterbrunnen Valley ( at about 800 t0 900 meters altitude) from Lauterbrunnen to Stechelberg. That brings you to the lowest station of the series of several cableways that can take to up to Schilthorn, via Mürren.
You can see that valley floor in the attached image, taken in a warmer month..