The biggest issue in regard to your question is that Canada didn't exist at the time of the Alaska Purchase. The Dominion of Canada was not formed until July 1, 1867, and the Alaska Purchase was approved in March of that year.

Canada as we now know it was a series of colonies governed by the British Empire, and as such, any Russian deal would have been directly with the British government, not Canada.

Such an arrangement would be incredibly unlikely. Thirteen years before the Alaska Purchase, those two nations had settled the Crimean War, and Russian foreign policy through much of the latter part of the 19th century (and indeed to a large degree in the first half as well) was geared toward limiting the power of the British Empire and seeking leverage against that empire.

Russia and the United States were very friendly from the creation of the latter nation to the end of the imperial period in 1917. When the Crimean War broke out, Russian-American Company officials prepared to make a "shadow sale" of colonial property to Americans in San Francisco as a way to protect that property during the war. The shadow sale never took place ─ RAC negotiators got the help of the Hudson's Bay Company to secure the colony's neutrality ─ but it appeared in the American press, and there began American interest in acquiring Alaska.

The Civil War and the Congressional deadlock that preceded it meant no action on a purchase could be taken before 1865. After Lincoln's assassination, and during the presidency of Andrew Johnson, Secretary of State William Seward had a chance to act on the purchase of Alaska.

In fact, Alaska was only one of several territories Seward pursued at this time. This was the period of Manifest Destiny, when it seemed that it was the United States' destiny to grow until all of North America was under the American flag. Seward was a firm believer in expansionist policy, and he attempted to purchase Alaska, Greenland, the Danish Virgin Islands and other Caribbean islands for the United States.

Only with Alaska was he successful. Congress was sharply divided between the radical wing of the Republican Party (which favored a strong line against the defeated Confederate states) and Johnson's moderate wing. The Democratic Party was largely discredited and had relatively little influence in Congress at this time. (In the House, for example, the Republicans had 175 seats combined and the Democrats 47. There were two Conservative Party members as well.)

The radicals had a rabid distaste for any policy by the Johnson administration (and would go on to impeach ─ but not convict ─ the president). Thus, Seward's dreams were stymied by political realities. Only through the liberal distribution of bribes (paid by the Russians) did the Alaska Purchase agreement get through Congress.

It was newspapers backing the radicals who created the terms "Seward's Folly" and "Seward's Icebox", but those terms were not widely used. Most Americans supported the purchase, as Alaska's vast timber resources were known, and it was theorized that there were extensive mineral deposits in the territory as well. (The Stikine Gold Rush had pushed thousands of gold-seekers across Russian territory and into northern British Columbia already.)

Incidentally, in the months between the purchase and the announcement of Canadian Confederation, there was a surge in interest in American annexation within British Columbia. Residents of that colony saw themselves surrounded, and with plenty of Americans within the colony (which was also facing an economic recession), many thought that becoming part of the United States was preferable to remaining part of the British Empire.