Unless the British were distracted with something else in their empire, you might be right.
It's hard to come up with something that would tie up enough British resources. I mean, the land factor is one thing (the Crimea is a war which calls on most of the British ability to deliver force overseas, which is why the British institute reforms which considerably increase their force projection ability) but the naval factor is, I think, impossible.
You'd probably need an all-out war with France to involve enough of the Royal Navy that what's left can't smash the USN and impose blockade. And even then I have trouble thinking of a good time for it - the Royal Navy was deliberately kept "far too strong" for the entire 19th century, and regularly launched and completed building plans to oppose French plus Russian "planned but not completed" building plans.
This isn't to say that what would likely happen is a blockade of the US. What would likely happen would be that the Americans wouldn't try anything at all, or if some filibustering expedition took place then the US would not support it for fear of trade difficulties.
So the OTL treaty which awarded Vancouver Island to the British was 1846. Altering that treaty is "easy" so let's ignore it.
Let's look a few years after that, to 1849 - imagine a crisis develops then, and the US is contemplating facing the British.
The US is essentially undistracted and has the previously established military from the Mexican-American War to draw on, so this is a good time for the US.
The first steam battleship as-built was the Napoleon, 1850, so everyone is still using wooden ships with sails as the battle-line form of sea combat. The US has of course got several frigates; so too the British.
The British also have a number of steam blockships, basically converted 74s with limited sea mobility (they fought OTL in the Crimea).
RN blockships (steam screw):
Blenheim (60)
Ajax (60)
(two others in conversion)
Ships of the line (sail):
Royal Navy
(First Rate)
(120)
Caledonia
Brittania
Prince Regent
Royal George
Nelson
Saint Vincent
Howe (BU 1854)
Saint George
Royal William
Neptune
Waterloo
Trafalgar
(110)
Hibernia
Ocean
(100/104)
Impregnable
Trafalgar (then Camberdown)
Princess Charlotte
Royal Adelaide
(Second Rate)
(98)
Dreadnought
Boyne (then Excellent)
(90/92)
Rodney
Nile
London
(84)
Canopus
Formidable
Ganges
Asia
Bombay
Calcutta
Monarch
Vengeance
Thunderer
Powerful
Clarence
(Third Rate)
(80)
Foudroyant
Waterloo (may be recieving ship)
Cambridge
Indus
Hindostan
(74)
Kent
Achille
Sultan
Armada class of 74s totalling 40 of which at least nine available
Cornwallis
Wellesley
Carnatic
Black Prince
Meiville
Hawke
Hastings
(Aside - not only is this list not necessarily complete, but at least one ship - Venerable - was not available because it had been converted to a church. That shows you how many ships the RN had, that they could give one over to be converted to a church.)
Thus, we can see the RN at this time has a plenitude of sail ships of the line.
USN
USS Franklin (74, receiving ship)
USS Columbus (74, recently out of Ordinary)
USS Pennsylvania (140, receiving ship since 1842, only sailed once)
USS Delaware (74, Ordinary since 1844)
USS Vermont (74, finished 1825, launched 1848) (...what?)
USS Alabama (74, finished 1825, launched 1864 as storeship)
USS Ohio (74, active commission in Pacific)
USS North Carolina (theoretically 74, receiving ship)
And that is it.
So the RN has at least
Two steam third rate
18 first rate
16 second rate
23 third rate
available, and the USN has
Three good condition third rate
Three questionable condition third rate
One poor condition first rate
and one third rate on the stocks
if it comes down to a question of ships of the line.
So the RN could, pretty much, match the USN's liner fleet with about 15% of the RN.
...hence, I'm not sure what kind of distraction would make the US actually go for it.
OTOH, the later you get the more populated Vancouver island is with Canadians and that makes it harder to do.... though the real population boom happened 1887 and on.