I know there is a plug-in for this (MoreInfo), but I am not allowed to use plug-ins, so I was hoping to do it within base NSIS.
No plug-ins at all? Or no plug-ins that that don't ship with the "official" NSIS installer?
In the former case will probably notice that your installer already
is using plug-ins, because many (basic) things in NSIS need plug-ins. Especially if you use MUI or MUI2, you installer definitely
does use plug-ins. And that's not a bad thing, it's simply how things work.
In the second case, why not use plug-in that does exactly what you need? Trying to emulate the same thing with the System plug-in of NSIS is much more difficult and more error prone! I'd rather trust a third-party plug-in than reinvent the wheel.
Anyway, if using third-party plug-ins isn't possible for whatever reason, writing your own plug-ins for NSIS isn't rocked science. If you already have a basic knowledge about C/C++ and you know how to use Visual Studio, you can probably implement it yourself in one hour. What you'd need is
GerFileVersionInfo plus
VerQueryValue and that's it.