Bear in mind that the time of year you are looking at is the end of ski season and that a lot of the usual passes that I would recommend for great summer hiking will still be covered in snow. Some of the passes and wanderwegs will be open albeit they will be covered in snow If you have the correct equipment and are interested in snow shoeing or hiking/climbing with crampons then this can be fun However, I would say if you are not experienced with this sort of hiking then please use a guide as you will be hiking over snow and ice and accidents can and do happen.

If you are looking for something at a lower altitude with less snow then I can highly recommend the national route 5 Swiss Jura though there is a chance that even parts of this route will be unpassable and still have snow as from what I remember there was still snow in some of the higher parts of this route in early May this year. The Creux du Van leg of the route 5 is a nice hike but even I wouldn't normally do this until end of April beginning of May.

Some sites you may find useful in planning your walks....

Activity Workshop

Wanderland

Zurich Hike and Outdoor of which I'm an organizer but to be honest most of the hiking doesn't start until mid/late April depending on snow/weather

edit - as an afterthought and going along with what Swisspea said, there is a nice hike along the river from Schaffhausen down to the Rhine Falls (approx 5-6km) and there are also a couple of valley walks in the Sargans area which should be fine and free of snow.