Looks like it was a mixture of both in the 90's.
According to Eliteprospect, Frank Jay was the Director of Amateur Scouting in Quebec before PL took over. Then when PL came aboard in 94-95, Frank Jay left, and they didn't have anyone in this title. Same thing their first year in Colorado in 95-96. Draper was just a scout at this time.
Then in 96-97 Draper took over as Director of Scouting. Then two years later in 98-99 his title changed to Team Consultant so he may have just run draft day. For two years they went without a Director of Scouting title, then Draper moved on to be Director of Scouting for the Coyotes in 00-01.
Then Jim Hammett took over as Avs Director of Scouting in 00-01. I distinctly remember this was much more of a part time gig than a full time one for him, maybe similar to Draper just running draft day. I think this is how they preferred things around this time.
Brad Smith had moved from Scout to Director of Player Personnel in 05-06. Hammett left in 06-07. They went without a Director of Scouting for two years, but Brad Smith might have handled this role. Then in 08-09 Pracey was hired as Director of Scouting.
94-95 - Empty
95-96 - Empty
96-97 - Dave Draper
97-98 - Dave Draper
98-99 - Empty (Draper Team Consultant)
99-00 - Empty (Draper Team Consultant)
00-01 - Jim Hammett
01-02 - Jim Hammett
02-03 - Jim Hammett
03-04 - Jim Hammett
04-05 - Jim Hammett
05-06 - Jim Hammett (Former Scout Brad Smith moved up to Director Of Player Personnel)
06-07 - Empty (Brad Smith might have handled this role)
07-08 - Empty (Brad Smith might have handled this role)
08-09 - Rick Pracey
09-10 - Rick Pracey
10-11 - Rick Pracey
11-12 - Rick Pracey
12-13 - Rick Pracey
13-14 - Rick Pracey
14-15 - Alan Hepple
15-16 - Alan Hepple
16-17 - Alan Hepple
17-18 - Alan Hepple
18-19 - Alan Hepple
19-20 - Alan Hepple
20-21 - Alan Hepple
21-22 - Wade Klippenstein
22-23 - Wade Klippenstein
Took a little deeper dive into the best picks during their tenures.
Pierre Gautheir (89-93)
Mats Sundin - 1346 games
Owen Nolan - 1200 games
Adam Foote - 1154 games
Bill Lindsay - 777 games
Eric Lindros - 760 games*
Anson Carter - 674 games
Andrei Kovalenko - 620 games
Alexander Karpovtsev - 596 games
Jocelyn Thibault (G) - 586 games
Adam Deadmarsh - 567 games*
Dave Karpa - 557 games
Todd Warriner - 453 games
Janne Laukkanen - 407 games
Rene Corbet - 362 games
Manny Fernandez (G) - 325 games
Frank Jay (94)
Milan Hejduk - 1020 games
Chris Drury - 892 games
Wade Belak - 549 games
Tim Thomas (G) - 426 games
Unknown (95-96)
Sammy Pahsson - 798 games
Marc Parrish - 722 games
Dan Hinote - 503 games
Brian Willsie - 381 games
Marc Denis (G) - 349 games
Brent Johnson (G) - 309 games
Dave Draper (97-00)
Robin Regehr - 1090 games
Alex Tanguay - 1088 games
Radim Vrbata - 1057 games
John-Michael Liles - 836 games
Martin Skoula - 776 games
Branko Radivojevic - 393 games
Ville Nieminen - 385 games
Kurt Sauer - 357 games
Scott Parker - 308 games
Brad Larsen - 294 games
David Aebischer (G) - 214 games
Jeff Finger - 199 games
Rick Berry - 197 games
Riku Hahl - 92 games
Steve Moore - 69 games*
Jim Hammett (01-06)
Paul Stastny - 1072 games
Brad Richardson - 869 games
Johnny Boychuk - 725 games
Chris Stewart - 668 games
Tom Gilbert - 655 games
David Jones - 462 games
Wojtek Wolski - 451 games
Cody McCormick - 405 games
Peter Budaj (G) - 368 games
Marek Svatos - 344 games
Brandon Yip - 174 games
Kyle Cumiskey - 139 games
TJ Hensick - 112 games
Brad Smith? (07-08)
Kevin Shattenkirk - 816 games
T.J. Galiardi - 321 games
Brad Malone - 207 games
Paul Carey - 100 games
Mark Olver - 74 games
Jonas Holos - 39 games
Rick Pracey (09-14)
Matt Duchene - 905 games
Ryan O'Reilly - 938 games
Gabe Landeskog - 738 games
Tyson Barrie - 683 games
Nathan MacKinnon - 638 games
Will Butcher - 275 games
Calvin Pickard (G) - 116 games
Michael Bournival - 113 games
Joseph Blandisi - 101 games
Joey Hishon - 13 games*
Alan Hepple (15-20)
Mikko Rantanen - 408 games
Tyson Jost - 342 games
Cale Makar - 178 games
Alex Newhook - 77 games
Bo Byram - 49 games
Martin Kaut - 20 games
Sampo Ranta - 10 games
Justin Barron - 7 games
Jean-Luc Foudy - 0 games
* Career cut short due to injury