You can use locally installed fonts in the Microsoft Office web apps. It's not obvious though, requires a little trick!
Download the Montserrat font family from the Google fonts site, open the zip, and go into the folder called "Static". Here you will find all the TTF files.
Open any of the Montserrat font TTF files in the font viewer, then take a note of its exact name. Write it down. And hit Install. Repeat for all the TTF files you want to install.
Here's an example showing Montserrat-Regular.ttf - the font name is just "Montserrat"

Open the Microsoft Word web app in your browser, and type some text, and highlight it.
In the font drop down you will not find the font listed, but you can type in the exact name of the font that you wrote down earlier.
Here's an example of Montserrat (installed locally) being used in the Word web app.
Click to see larger
The only real downside to this is that you need to know the exact names of the fonts so you can type them in manually. You also need to type the exact name with no spelling mistakes, or it won't work. Note that anyone else viewing the file will also need to install the fonts locally on their computer. Such is life though!!