I'm betting that the Hawken has a 1:48 twist barrel. Therefore, I'd say conicals would likely be your best bet. I had good luck with Maxi-balls in 425 gr in my 1:48 twist Renegade; however I've heard that the quality of the Maxi-Balls are not what they used to be and I haven't used them for over 10 yrs....... I'd try Precision Rifle bullets if you can find them.
http://www.prbullet.com/chart.htm Probably the Keith Nose in 300 grain.
Another option would be PowerBelts. My Renegade shot the 348 gr hollow point bullet well, but I didn't like how soft the lead was and how it pancaked on a deer. Powerbelt makes a copper jacketed bullet that should work better than the all lead ones that I tried before.....(I haven't used my Renegade since the rules changed allowing jacketed bullets).