no shortcuts will not slow anything down at all and I would not worry about them either. you can make a short cut to any program on your pc, just like how you have the icons on your desktop those are all shortcuts that lead to the real program, so they are just like a little bookmark. Do not take up any space and do not slow things down.
How many icons do you have on your desktop?
I can not imagine why it would say you have that many invalid shortcuts.

It is often from programs you may have had on the pc and removed or something you changed or updated usually everything you install asks if you want to add a shortcut somewhere, usually the desktop.

if you want to pursue elimination of them then you might want to try this free program that will list all of them and let you pick and choose what to eliminate.
OrphansRemover

as always once you download any program right click on it and scan it with your AV and antimalware programs to make sure it is safe and clean before double clicking it.
Remove Invalid Windows Shortcuts

I have 8 shortcuts on my computer that I use. Some I use every day.

I did a basic Google search using the key words "invalid shortcuts" (sans quotes). A plethora of responses identified them, made suggestions and explained how to remove them. You might want to give that approach a try first to become informed before making any decision.

DA

Thanks for the information I will check it out.