I believe this is from the '02-'03 season looking at the all-time Blue Jackets numerical roster.   
19 - Mathieu Darche  
37? could be 33 hard to tell - Looks like 33 Jamie Allison 
14 - Ray Whitney 
12 - Ted Drury 
25 - Andrew Cassels 
8 - Geoff Sanderson 
48? could be 45 - It's a 45 Jody Shelley  
7 - Scott Lachance 
22 - Chris Nielsen 
78? could be 70 hard to tell - No one has ever worn 70 or 77 for the CBJ   
Also was a 17-Tomi Kallio 
Also was a 5- Jamie Heward   
That's all the ones I'm for sure on.  I had nothing to do, but if you gave me better pictures I'm sure I could do all of them.    
If I had to guess, this was signed before the '02-'03 season or right at the beginning of it.   
I'll give you $80 for it though.  It's really not worth a ton.  I didn't see a Nash signature, but I saw one that looked like a 61, 51, or 31.  Didn't look like Nash though.  You can see the amount people ask and the amount they take, not many people are willing to spend hardly anything on this especially without a COA.  You'll be waiting about 50 years to get $1k for it, and that's only if the team starts to become a huge success.   
EDIT: just to show you how much signed hockey sticks are worth, check out Ebay.     
http://cgi.ebay.com/1980-USA-HOCKEY-TEAM-AUTOGRAPHED-RARE-HOCKEY-STICK_W0QQitemZ110449682494QQcmdZViewItemQQptZLH_DefaultDomain_0?hash=item19b750683e 
1980 USA "Miracle" team signed stick, Buy it now $450