Sounds like you’re jumping to a conclusion without understanding the problem.
You say the problem is that playing movies from your Synology NAS sometimes stutters, and that faster storage will solve this problem. For starters, it’s playback of movies from the Synology to… what, exactly? To your television? To your Mac Mini? Most Synology NAS systems support 1 Gb/s Ethernet. You aren’t playing 1 Gb/s movies, so perhaps the problem is your network speed.
You could investigate two possible solutions: First, just use Ethernet instead of WiFi. Second, if you can’t use Ethernet, test your speed to the Synology and figure out how to make your WiFi faster: You could move the router, you could flip the Mac Mini upside down, you could try removing devices attached to the Mini to see if they’re causing interference, and relocate them with longer cables if needed.
Any of these solutions is a lot less complicated and expensive than replacing all of your storage.