The "old" way would be to localise the glob.

open (IN, "file1") or die("can't blah blah");
while (<IN>) {
    print;
    print slurp();
}
sub slurp {
    local *IN;
    my $slurp = do { local $/ = undef; open IN, "file2"; <IN>};
    return $slurp;
}
[download]

But these days you can use lexical filehandles.

open (my $in, "file1") or die("can't blah blah");
while (<$in>) {
    print;
    print slurp();
}
sub slurp {
    my $slurp = do { local $/ = undef; open my $in, "file2"; <$in>};
    return $slurp;
}
[download]

Or, as you point out, you can use FileHandle or IO::File.