In historical order (and only NHLers, not including pre-NHLers & Soviets):
1. Frank Nighbor ("The Flying Dutchman")
2. Max Bentley ("The Dipsy Doodle Dandy")
3. Jean Beliveau
4. Gilbert Perreault
5. Alex Kovalev
6. Pavel Datsyuk
Six, sorry. I can't decide whom to cut.
Datsyuk was a lot like Nighbor in terms of exceptional two-way use of the stick, Perreault like Beliveau in terms of size and movement north-south, Bentley arguably the best of the bunch in terms of historical accolades and descriptions and Kovalev had staggering stickwork but flaws in other areas of his game.
Cut Kovalev and Datsyuk, add Bobby Orr.
Does anyone else have Alexei Kovalev's stickhandling DVD? We tried some of the exercises when it first came out, but it came out 10 years too late to do me any good.
...add Bobby Orr.
Canada’s Top 100: The Greatest Athletes of All Time said:... Morenz dominated the ice with his aggressive play and dazzling stickhandling...
Canadiens Legends: Montreal’s Hockey Heroes said:His spectacular rushes and brilliant stickhandling lifted fans out of their seats.
Joe Pelletier said:Syl Apps ranks as one of the greatest captains in Toronto Maple Leaf history. A team captain from 1940 through 1943 and again from 1945 until his retirement in 1948, Apps was the star of the 1940s dynasty that captured 3 Stanley Cups with him at the helm.
Apps was an artistic a player as have ever played in the National Hockey League. They called him the “Nijinsky of the Ice,” comparing his graceful skating abilities to the happy feet of the great Russian ballet dancer Naslav Nijinsky. Equally as impressive were his puck skills – he had one of the most accurate shots and loved to set up his teammates – particularly Harvey "Busher" Jackson and Gordie Drillon. He could do tricks with the puck as he stickhandled down ice unlike almost any player of any era. Comparisons to modern day superstar Joe Sakic are not without merit. Several of the few old timers who are still with us insist Syl was the greatest player they had ever seen.
Syl Apps deserves mention in this thread.
Soviets: Firsov, Kharlamov, Makarov,
Soviets: Firsov, Kharlamov, Makarov, Maltsev, Balderis, Vikulov... probably forgot smbody
Overall, Petrov wasn't as smooth as those players you mention, but I think he was an excellent stickhandler and deserves a mention; he didn't mishandle the puck much and I've been especially impressed by his hand-eye coordination (he could catch pucks out of the air effortlessly). But there are so many Soviets that were brilliant stickhandlers; not too many 'hands of stone' that I can think of.
I never considered Petrov as a great stickhandler - you'll barely find anything highlights worthy of him in this department (and it's pretty easy to do with any of names I mentioned). Petrov's highlights will be all about his absolutely unbelievable passing abilities - his vision was just sensational.
I don't think, there were a lot of great stickhandlers in the NHL before they started regularly play vs Soviet teams in 80s. Classic Canadian hockey was all about toughness, physical pressure, hard shots and playing around the nets.