The cabinet meeting in late July on whether to declare war was almost evenly split.
Cant remember who the "doves" were, but Churchill (unsurprisingly) was one of the "hawks".
One description I have read is that in cabinet on Friday the decision had been not to declare war.
But by Monday 3rd August, without any meetings or major events taking place, the mood had changed.
Removing the decade long naval buildup & rivalry could have been enough to change that enough, at least in early August.
Impossible to rule out a later declaration or involvement.
The UK hadn't intervened in any of the European wars of the 19th century, with the sole exception of the Crimean war.
And there were quite a few:
https://en.wikipedia.org/wiki/List_of_conflicts_in_Europe#19th_century
So, having not intervened in any of the others, from the viewpoint of 1914 there wasn't a huge amount of difference about this one, from the Franco-Prussian, Prussian- Austrian, or Franco-Italian conflicts of the previous 100 years.
I find it hard to say categorically that no naval rivalry results in no declaration of war, or that war is inevitable.
From what I have read I think that the OTL declaration was unexpected by Germany, and was greeted with relief by France and Russia.
Which implies to me it was not seen as a certainty.
Remove half or more of the high seas fleet, and in my view that near certainty becomes something closer to somewhere between probable and possibly.