How about the following:

if (my @words = /(\b.*?\b)/g and not grep {/\d/} @words) {
  print @words;
  # Do stuff.
}
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However, having two regex isn't always a bad thing. Personally, I think your code reads easier and is more intuitive; my only change would be from if (/^[^0-9]+$/) to unless (/\d/)

 
perl -e 'print "I love $^X$\"$]!$/"#$&V"+@( NO CARRIER'