A difference between the 'my' function and the 'local' function that is not immediately obvious after reading their descriptions is illustrated by running the below snippet. It shows that 'my' is a bit more powerful, it keeps the variable's value completely within the block. While local allows calling subs to also access the variable's value within that block. Unless there are areas in your program that _expect_ this behavior, you should be fine changing everything to 'my'.
print "localVar is : $localVar \n";
print "myVar : $myVar \n"
$localVar = "I am localVar.";
$myVar = "I am myVar.";