Shortening to Swiss Buttercream
Yes, shortening can be used in Swiss buttercream. Comments on an online article suggest a couple of good reasons you might want to:


The buttercream will hold up better in warmer weather than an all-butter recipes;
If you want a pure white "buttercream" then shortening is the way to go.


The same article notes that some tasters didn't appreciate the buttery aftertaste of a low-sugar recipe. A vegetable shortening like Crisco is practically tasteless and could be used to fix that problem although you presumably want at least some butter taste in your buttercream.

In various other places online I see comments stating shortening should not be used. Mostly this advice is given without any clarification of what might result, but I saw one suggestion that shortening is responsible for the greasy feeling that some buttercream leaves on the roof of your mouth.

There are actually not that many Swiss buttercream recipes online that include shortening, but I decided to average out the proportions of those I did find to come up with this weight ratio:


  1 : 2.2 : 2 : 0.7 (egg white : sugar : butter : shortening)


Or, to make ~1kg of buttercream,


  155g, 150ml or 5 egg white where each egg white is 31g
  349g or 414ml sugar
  332g or 328ml butter
  109g or 125ml shortening


I ignored that some recipes use either granulated sugar, confectioner's sugar or both.

I whipped up a batch with these proportions and the result has a pleasant butter flavor. I didn't detect the greasy mouth-feel I had been warned about and although I don't have a piping bag handy I can tell that it will pipe just fine.

Since you asked for a ratio you could do worse than start with that I've given. 

Side note: if you do use this ratio I screwed up dissolving the sugar, so you might either want to use slightly less sugar, or leave it on the bain-marie a while longer. Either way, don't do like I did and just assume the sugar has dissolved.