Hi Nityasingh -
<<"April usually marks the beginning of Spring and the weather is neither
too cold or hot, but if plan to hike in the mountains, some trails may
still be inaccessible.">>
The first part is certainly true at lower altitudes.
But, as you go to higher altitudes, such as the villages ( around 1100 to 1600 meters) and trails near the Jungfrau , Spring is really delayed until late May or June. It gets colder as you go higher. Nice trails at around 2000 meters don't open until mid-June. April usually still may have some skiing at the beginning of the month, during the time you are there. After that, there are fewer visitors, and some of the tourist facilities close for holidays or maintenance. Just to illustrate with one typical example, April 12th, 2020 is the last day that the Hotel Schonegg in Wengen is open until May 29th. Others remain open, but in the high Alps, you will be at the tail end of Winter. Winter hiking trails exist in the Jungfrau region, but they tend to be maintained only until late March, as the snow conditions deteriorate after that.
At low altitudes - places such as Luzern, Zurich and Interlaken itself, will indeed see the start of Spring in April.
I've not been to Zermatt or St. Moritz at that time, but the areas in the mountains around Zermatt (1616 meters for the town) are at higher altitude than those near the Jungfrau. Gornergrat is at about 3000 meters. You cannot visit the Matterhorn, but there are great views from Riffelalp and Gornergrat.
St. Moritz is at around 1820 meters. You'll almost certainly have snow there. Not sure about the exact conditions on the valley floor, at about 1770 meters. Trails on the valley floor will usually be maintained.
So, with you itinerary, you'll experience some conditions more like Winter,as well as the beginning of Spring, depending on altitude.