To add to what the other monks have said ...

There's an error and at least one weirdness in your code:

1. the next line works by accident. It's checking if $filename in the current directory is a directory or not. If there happens to be a directory in the current directory that has the same name as a file in your summary spr directory, it will be skipped.
2. your map-in-void-context looks like it might just be trying to act as chomp. If so, it's just chomp(@{$sspr_hash{$file_name}} = <FH>); with no map afterwards.
3. grep works on lists but you're only using it on a single item. Valid but strange. Typically people would just do $line =~ /$old_schema/i

Also, I'm not sure why you've divided your task into two parts like this. Is there a reason you're reading the contents of the files before you do any processing? If not, I'd just do it all in one go like this:

#!/usr/bin/perl

use warnings; use strict;

my $ssprdir = "/apps/inst1/metrica/TechnologyPacks/ON-SITE/summaryspr/
+";
opendir(my $sspr, $ssprdir) or die "Can't read $ssprdir - $!\n";
my @files = grep { ! -d $_ } map { "$ssprdir/$_" } readdir $sspr;
closedir $sspr;

for my $file (@files) {
    unless (open(my $fh, "<", $file)) {
        warn "Unable to open $file - $!\n";
        next;
    }
    # ...
    while (<$fh>) {
        next unless /$old_schema/i;
        #  ...
        print "$old_schema|$new_schema_str|$found_status|$migratestr|$
+rename_str|$file\n";
    }
    close $fh;
}

__END__
[download]

Also, if $old_schema is really supposed to be a string and not a regular expression, you might consider using index instead of engaging the RE engine.