However AM said that they had a hash of sub names, possibly from a external library. If you cannot convert the hash of subroutine names to a hash of code references  $s{key}=\&valsub; then use a bare BLOCK to turn strict off only when calling subs from that hash:

{ # Get an enclosing lexical scope
  no strict 'refs'; # allow symbolic refrence shenanigains
  &$SubHash{key}(); # Call sub
} # Back to strict 'refs'
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or write a sub for this purpose (This assumes $SubHash is a global)

CallFromHash {
  no strict 'refs'; # allow symbolic refrence shenanigains
  return &$SubHash{shift(@_)}(@_); #Call the sub in the first arg with
+ the rest of @_ as args and return
}
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However a hash of sub names is probably a bad idea to start with, and you should reconsider your design to use hard refs (mentioned by Joost) or remove the hash all together if possible.
Update: Forgot Amperstands