If the cache needs to be shared among children - I second the vote for memcache.

If each child needs its own, I'd do something like the following using the End module:

# add clear_cache method to your sharedcache
package sharedcache;
sub clear_cache { $cache = undef }


# inside your apache handler use the following:

use End;
sub handler {
    my $clear_cache = end { sharedcache::clear_cache() };

    # normal handler operations go here
}
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When your handler goes out of scope - the object stored in $clear_cache will go out of scope and the stored coderef will fire - clearing your cache.