John,
I think you have hit the nub with your concept of the tyranny of time & distance in this period. It was a lengthy process to compose a formal declaration & use either a special envoy or an accredited ambassador to issue it to the other belligerant power. And, of course, not a necessarily advantageous way of beginning to fight.
However, I think you will find the full gamut of approaches to war in the period: from the pre-emptive strike to the formal declaration.
Take a look at the British-Spanish hostilities that began in 1804 at the end of the Peace of Amiens.
The British reacted to Spain's efforts to stay neutral by paying Napoleon a subsidy as an hostile act. They did not chose to declare war formally & alert the Spaniards but opted to commit an act of war bysending a squadron under Moore to seize the Treasure-Fleet.
The Spanish responded to this by formally declaring war a month later.The document was sent to Britain.
I have read several Spanish declarations. They are, as you would suppose, formal, lengthy & present a case for belligerance.
E.G "That ambitious & greedy nation (Britain) has once more proclaimed to the world that she recognises no law but the aggrandisement of her own trade...."
I would think that this was the form of any declaration in the period.
As for Austria in 1813, following the abortive negotiations in Prague,Metternich isued a formal declaration against the French.
I have not read it but according to Zamoyski, it was a "document full of mournful complaints detailing how (Austria) had been wronged by France".
donald