For flowers and other piped decorations it is probably best to use American buttercream or American buttercream with the addition of egg white powder. I’ve never used Swiss or Italian buttercream so I can’t help you with that. My personal preference is ermine or cooked flour buttercream.
I refrigerate my SMBC frosted cakes, they are generally just for my husband and me, and if allowed to come to room temp, the frosting is fine.
I have covered cakes in smbc, and not refrigerated at all. I’ve also covered smbc cakes in fondant, and again, did not refrigerate. A smbc cake is fine for 2-3 days unrefridgerated. Only time I would put my cake in the fridge is because of excessive heat and humidity.
I refrigerate all cakes, habit probably.
I refrigerate all my Italian meringue buttercream cakes overnight and suggest they be brought to room temperature for serving. On wedding cakes I have done the same thing and since delivery is usually a few hours before the ceremony and reception the cake and icing are at room temperature and ready for cutting and serving.
If you’re concerned about food safety, Swiss meringue buttercream has enough sugar to keep it safe at room temperature for several hours. If your concern is about the buttercream and piped decors melting, using unsalted butter makes a more stable buttercream.
I use smbc all the time and it’s fine out for several days (I’m in the UK though so obviously I’d you’re in a warmer climate this wouldn’t hold true for that length of time).
Normal butter can be left out of the fridge for up to 10 days, so add in a ton of sugar and a few days is fine. I should add I do not leave my smbc out for 10 days (although my personal use butter does stay out for many days), just illustrating a point.
The only time I’ve put mine in the fridge was when we were having a heat wave this summer, then I gave it 2hours to come back to room temp before serving (due to the heat this was plenty of time).
Imbc is I believe a bit more stable, but I’ve not made it for a long time so can’t compare. If you ever watch Anne Reardon (how to cook that) she has a YouTube video comparing several types of bc, including how they hold up under heat. It might be useful to you :)