I don't know quite what you mean by 'Schweiz to Andermatt'. Schweiz is simply the German name for Switzerland. Schwyz is a Canton through which part of the Zürich to Andermatt routes goes. (please wave to my daughter when riding through Goldau)
What exactly do you mean by road bike?

Zürich to Andermatt.
Had a look at this route with my husband. He can see no part which is unsurfaced, but he says that if such a part is on the route, there is a way round it. Apart from that he has, with his racing bike, never, ever had a puncture on 'unsurfaced' routes which are basically simply not tarmac. Could be gravel, could be hard-packed earth.
It is difficult to give 'advice' when we know nothing about your wishes or ability and experience. My husband says that Göschenen to Andermatt nach 100Km is narrow, steep, busy, (when the Gotthard is open, but it isn't), hot and tough but perhaps you're much younger and super fit. Kurt says he would opt for train for that last bit.
If you do go, have a good day!
From Zürich there are 100km runs in all directions, also things which are better from a traffic point of view than the Axenstrasse. (Lies on your route) There are bicycle maps for racing bikes and mountain bikes which show gradient, busy roads and unsurfaced roads too. Bookshops stock them.