While it's not at all clear that adding 'use strict' will magically turn up the bug (it's more likely that adding 'use strict' will fail to compile large sections of the code that don't contain the bug your looking for, and that the bug, if at all present, will persist, even if you make it up to stricts standards), adding 'use strict' is quite simple.

Just copy the module(s) to a directory where you do have write permission, add 'use strict' in the copy, and put the directory in your PERL5LIB environment variable, then run your program. It should now pick up your copy (with 'use strict') instead of the original. And since 'use strict' only has compile time effects, all you need to do is run 'perl -c' on the (copy of the) module - don't even need to run your program.