Bummer you don't want curvey mountain driving as you will miss some really great scenery however...
From Laramie, going south on US 287 to Ft Collins, then I-25 to I-76 to I-70 westbound at Denver will get you over the continental divide with about the fewest curves to deal with. There are substantial grades on these roads.
If you want to avoid switchbacks, don't go on US 40 over Berthoud Pass... lots of switchbacks on that road till you get to Winter Park, then it's a cakewalk.
By going through the I70 tunnels, you can get to GL via Colorado route 9 at Silverthorne to Kremling. There are plenty of curves on this road, but not a lot of switchbacks. It is definately the long way, but you set the road requirements.
If it was me, I'd head out of Laramie on Wyoming state highway 230 to Colorado highway 125 north of Walden. Stay on CO 125 'till US 40 near Grandy, go east on 40 to US 34 then north to Grand Lake. This route misses Denver and the entire front range traffic nightmare. It is mountain driving and if you are uncomfortable, I guess a heavy traffic route is your best choice.