Cath, I am so sorry to hear of your loss. My condolences.
So a cantonal/Gemeinde/local YMMV:
In my Schwzyer Bezirk, the certificate of inheritance is applied for, and produced, by the Erbschaftsamt. They are adjacent to the Bezirk Notariat, but a separate niche. I bring this up because in my experience, starting a process with the wrong official can mean delays. (Just finding out who was responsible for what was difficult IME.) So if your Gemeinde/Bezirk has that separation of responsibility, go directly to the Erbschaftsamt. The process should be outlined on your Gemeinde website.
A copy of your husband’s Testament is needed. If one does not exist then you’ll need to provide names and addresses (if known) of all the potential heirs.
FYI, you will probably be asked for copies of your husband’s passport (if not Swiss) or an excerpt from the Familienausweis/Familienbuchlien (if Swiss). Possibly also your marriage certificate, or excerpt from the Familenausweis showing your marriage, if your husband was Swiss. If you need to order excerpts from the Familienausweis, extra time might be needed. These are ordered from the Zivilstandamt. (Again, my Bezirk, may be done differently elsewhere)
FYI, the certificate of inheritance might be costly. Before you order a dozen copies, though, we found that only one or two official copies were needed - most institutions requiring the certificate (banks, pensions, etc.) accepted a photocopy.
I would not hire a lawyer if there is a will and you do not expect conflict among heirs. Rather, if you need someone to do the ‘running around’ with bureaucracy, do you have a trusted friend here that you could delegate it to?
So much of the process is ‘hurry up and wait’, which if a lawyer’s meter is running can get expensive. My experience is that even with a lawyer, much of the running around still falls to the principle heir.
I found that most things had to be done via mail anyway, so do-able for you from afar if you can get them to tell you exactly which documents are needed. BTW, many of the forms needed can be ordered from the website of the responsible bureaucracy.
If, however, you anticipate conflict, engaging a lawyer can be prudent.
Again, I am so sorry, Cath.