We have to take into account not only Skyrim's geography, but also its industrial capacity and its agriculture.
Apparently the focus of the region is on the export of arms and raw materials. Skyrim does not have strong agriculture and would not be able to support itself, as both the number of farms is meager, and the number of mouths to feed is high, even though it is a region with few inhabitants, but even with few food production is very low.
So probably a large part of the food that circulates there must come from the capital of the empire and practically all the maritime trade also corresponds to financial agreements with the Empire. High Rock should not represent much of that percentage, as it is a small land with small towns, almost the same as Skyrim. So, therefore, the region must declare independence before, it should focus on its industry and mainly on food production.
Nor can we fail to mention Skyrim's main evil ... his Jarls!
Arrogant, self-centered, ignorant and wasteful. This represents the leaders of Skyrim with one exception or another perhaps. And these same ones would not accept to change their lifestyles to invest in their own counties (something that for almost all the time since they took power, they never did). They will continue to give high and expensive banquets, in addition to continuing to spend what they cannot collect for a long time. This will further contribute to the breakdown of the region's economy.
We also have the fact that the Civil War drives tourism and travelers away, since who would like to venture into a land at war? We, the players, who were caught right in the middle of this war are the clear example of what this represents. And we almost had our heads cut off just because we were in the wrong place at the wrong time. So that being the case, and knowing that they may experience the same situation, which is quite obvious, few will risk going to Skyrim.
So with all of that, it is very likely that Skyrim without the Empire is not only unable to support itself, but it will not last long. It is very likely that the counties will decline, other civil wars will ravage the place, as Ulfric was only focusing on having a crown on his head, but did not prepare the region for the post-war period. So many Jarls will revolt against their Government and new wars will ensue, further destroying the region and turning Skyrim into a cluster of ruins (more than it already is).
Skyrim without the empire, due to lack of planning, cannot last. Who are you going to sell your raw materials to? Hammerfell is in no condition to have a trade with Skyrim of the same level as the Empire, considering that they are still rising after the war against Aldmeri dominion. The Thalmor would never make trade deals, since they were probably responsible indirectly for the Civil War, because of this, they want Skyrim to break down and they would have no reason to trade with them. High Rock is still part of the Empire, so they would be pressured not to enter into economic deals with the Nordics. Morrowind? Many even question whether that place still exists, a land completely desolate and destroyed that is slowly rebuilding. They would not be able to trade with anyone today. They can hardly keep Solstheim.