These icons appear to be rendered (on the fly) as they are animated. This indicates that there is no static icon file that you can edit or delete. I use both OneDrive and Skype, both have animated icons and neither can be removed from the Menu Bar.
It appears (IMO) that this is a design decision by Microsoft because their Menu Bar does more than just give you access to sub-menu items; the icon(s) displays status like "Away", "Do Not Disturb" or "Invisible". More importantly, it shows whether you have connectivity or not.
Speaking from a perspective of been a Product Manager for both hardware and software, it's entirely plausible there were folks who removed the icons from the status bar only to complain to Microsoft that they needed a way to know if they were "Away" when they didn't mean to be. I don't know that this happened, but I've seen similar in my own experience.
I see that Microsoft has been ignoring the same question from many
user, for years. MS Forum.
Putting on my pragmatic hat here for a moment, since the 23rd of Nov. 2017 when the thread was created, there's only 183 people that identified they had the same question.
There are approximately 1.67 billion Skype users world wide*. To put that into perspective, that's a percentage of 1.01 x 10-7 or 0.000000002%. This is a very small population over approximately a (roughly) 26 month period!
If we compare it to the outstanding feature requests the top request at this time has 1,250 votes and that's only the 1st one. If I tabulate all the requests greater than 183, you're looking at 4,750. This issue is just 4% of that total.
Keep in mind that this is not considered a bug or a problem (as nothing is broken) but a feature request (yes, it's a "problem" to you).
What does all this mean?
It's an annoyance and you'd like it gone, but given where it ranks in the grand scheme of things, it's not likely to get implemented. The squeaky wheels get the grease and this issue barely has any squeak.