As always, there's more than one way to do it. Also, it depends on which features you need, and whether you would be able to change a bit of your setup.
You could just build a new package containing your own CharName.pm and install it. Strawberry Perl contains all the tools you need. I don't know why your PERL5LIB has a different ordering of the vendor and site paths than usual - you might need to reverse that.
You could also check whether the core module charnames fulfills your needs. It is as up-to-date as your Perl version: Unicode version 5.1 came with Perl 5.8.9. It provides character names with the charnames::viacode function but no equivalent to the ublock.
I think the PERL5LIB path is weird since normally it isn't needed - it's in @INC. But OP is using the Git for Windows perl, not Strawberry (C:\Strawberry\Perl\bin\perl.exe) but wants to use the libraries installed in Strawberry with the Git for Windows perl. So he has to configure PERL5LIB with paths that would normally be in @INC, but the Strawberry paths aren't in the Git for Windows perl @INC.
A bit of kludge if you ask me, I just use PowerShell (way more capable than cmd.exe and can be customized to be like bash) so I don't need to use Git for Windows bash and thus never have the perl conflict issue.
Actually, when I said "My .bashrc sets $PATH to Strawberry perl" I should have quoted my (now modified per ^2) .bashrc:
if [ -x /c/Strawberry/perl/bin/perl.exe ] ; then
export PATH="/c/Strawberry/perl/bin:/c/Strawberry/c/bin:$PATH"
export PERL5LIB=/c/Strawberry/perl/site/lib:/c/Strawberry/perl/vendor
+/lib
fi