I am not completely sure in this particular case, but with PerlApp, often the answer is to add more "use" statements, like this:
PerlApp uses the "use" statements to decide what to include into the .exe. If this file is part of the base module's manifest, then this will work. Give it a try and let us know what happens. To force a random file into the .exe with PerlApp like perhaps a .gif that your user code needs, it is easiest to start the GUI version (perlapp with no parameters). If memory serves me correctly, there are some obvious options to select a file. However for the program itself, try the above first.
Update: here is a node where a similar suggestion worked: PerlApp and Win32::Unicode The OP's question is a bit different, but close enough that an attempt is warranted.