Inheriting is always sad, because someone passed away, so, first of all, I'd like to express my condolences.
But it's of course nice to get into the possession of such a comforting sum of money. It's a very defensive portfolio, which seems well adapted for someone with a very low risk-tolerance and a very short term outlook, where immediate wealth preservation is the ultimate goal. This means it was probably well suited for the 'previous owner', but not for you.
With roughly 1 million CHF it's still a relatively small sum than can easily be self-managed, but one that is also big enough to use some more advanced strategies, if that is your goal. But you have to decide if you want to actively manage your own portfolio, which is time consuming, or if you are more looking for a setup and forget solution.
The setup and forget option would be a basket of ETFs, where you have a wide range of options: going for some split of low TER (this is the annual cost of an ETF) broad market ETF like WEBN or SPYI (all world all caps), or, to reduce US exposure, more something that tracks stoxx600 for the European market or Swiss centric like SMI, SPI, SLI. These can all be mixed to your liking. You can of course also add other regions, depending on your economic outlook. To reduce volatility, you can even add some ETFs that contain bonds / CDs of different maturity. And you can also keep some gold or diversify even there into other precious metals like silver, platinum, or palladium. Gold is a decent inflation hedge, the other metals are higher affected by the economic outlook, given their industrial use. Also BTC can be considered, even though it is strongly volatile, but it is also uncorrelated to various external factors. I would buy it directly on a reputable exchange like Bitpanda Fusion, and then move it to a cold wallet à la Trezor, and not in the form of an ETF. A mix of these things don't need your attention and can just grow over time, if your time horizon is 20 years or more.
There's too much to type about actively managing your own portfolio, instead, I'd like to put another idea out there: real estate. Land is a limited ressource, and you have the funds now to even get a little house with maybe 2-4 apartments to rent out (depending on the location, of course).
Best of luck!