ericleasemorgan,
You're data structure doesn't allow short circuiting. You could do a 1 time pass of %words and create a parallel data structure that would make subsequent searches a hash lookup. Something like this:

my %stems;
for my $word (keys %words) {
    my $stem = $stemmer->stem($word);
    $stems{$stem} += $words{$word};
}
for my $idea (@ideas) {
    my $stem = $stemmer->$stem($idea);
    my $val = $stems{$stem} || 0;
    print "$idea\t$val\n";
}
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Of course, if %words is constantly changing then so must %stems. There are ways to do this (tied hashes for instance) or just a better datastructure (tree versus hash). As far as better stemming library - the library you are using does support exceptions. When you say you are going to run the program 10K times, it makes me wonder if you mean each time it is only going to get the value of a single word. That would obviously be inefficient. It would be better to serialize (freeze/thaw) your data structure so you don't pay the runtime performance penalty of converting the hash.