Seems an ideal application for threads. Something like this should get you started. You'll need to fill in the blanks.

#! perl -slw
use strict;
use threads;
use threads::shared;
use Thread::Queue;

my $logSem :shared;
sub LOG {
    lock $logSem;
    print @_, "\n";
}

sub worker {
    my( $Q ) = @_;
    require Net::Telnet;
    my $tn = Net::Telnet->new( Timeout => 10, ... );
    
    while( my $apip = $Q->dequeue ) {
        if( $tn->open( $apip ) ) {
            LOG( "$apip OK" );
            $tn->close;
        }
        else {
            LOG( "$apip: Failed" );
        }
    }
}

our $W ||= 15; ## Default to 15 threads; Don't get carried away!

## Create a Q to supply workers with work
my $Q = new Threads::Queue;

## Create the worker threads, passing the Q handle
my @workers = map threads->create( 
    \&worker, $Q
), 1 .. $W;

## Push the IPs onto the queue
for my $foo ( %controllers ) { ## ???keys values???
    for( @{ $controllers{ $foo }{ access_points } } ) {
        $Q->enqueue( $_ );
    }
}

## Terminate worker loops
$Q->enqueue( (undef) x $W );

## Wait for the workers and join them when they're done
$_->join for @workers;
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If your serial code takes 15 minutes, this should reduce it to ~1 minute. But don't get carried away increasing the number of threads, as there are diminishing returns.