I've been up to Alaska and back twice in my Husky, as well as two trips
to Canada.
There are usually tailwinds up the coast and tail winds down the Alaska
highway, or the more more scenic but less historical Cassiar highway
(through Smithers). The coast in the summer is doable, but cloudier
than inland. There really is no way to know where the best weather
would be. I would fly where the good weather is. Any and all of the
routes are doable in a small airplane, though the Coast route does not
follow a highway. There are three highways connecting the inland to the
coast, all are mountainous.

Canada permits longguns, essentially no pistols. There is a $50
Canadian fee and you have to declare them. Although there is a rather
outdated, almost never enforced rule that you have a radio permit, if
you doon't have one, don't bother. No one asks. I'd recommend carrying
some food and survival gear, though it is not mandatory. Pistols are ok
in a plane in Alaska but how are you going to get it there? No
concealed carry on your person without permits in Alaska. Basically if
you bring a gun, a shotgun makes the most sense and is the most
politically correct. I've haven't been bothering, never have needed
one.

To cross the border, file a US flightplan and call Canadian Customs. It
is easier to clear Customs at an airport that is not major, but is
still big enough to have a full time Customs officer, so he doesn't
have to drive in. Better to be a little late than early with your
arrival. Flight plans are pretty much mandatory in Canada.

Sporty's or some similar place sells charts, and you need the Canadian
equivalent to the US Airport Facilities book. I used WACs and my
updated GPS. Flying under Canadian rules is not a problem, there are
some differences but not much.

Go ahead and plan your flight, but be prepared to change your plans
because one route can be weathered in and the other routes still
flyable.

The coast route is the most scenic and adventurous especially if you
fly over the mountains to get there from inland. The Cassiar highway is
more scenic than the Alaskan highway, but the Alaskan highway is more
"historically interesting". But all three routes are doable, along
with various combinations, though the coastal route is over water for
at least some of the trip. You are going to have to fly over some water
to get to Juneau, so you will be exposed to water anyway (unless you
come in HIGH right over the mountain wilderness from the east, no road
to follow and some of the MOST remote terrain I've ever seen). There is
no road that connects Juneau to ANYWHERE. When you fly the coast you
are usually flying over water but near land. This is true for the
entire route. If you go to the coast count on getting weathered in for
a day or two somewhere. Statistically July 4th is th clearest weather,
certainly is the warment week of the year and has looong days.

The trip is certainly doable. Get your aircraft in the best shape you
can, buy the charts, update your GPS and go. It is a fantastic trip!