They argue that:
"We have been preparing for independence fo 75 years and we have our backs covered on all issues. It is about breaking up the political union, not the Union of the Crowns."There is however a small issue to be considered; that of language.
The United Kingdom as a term came into being and usage in 1801, with the Acts of Union
The United Kingdom first became the name of the Country in 1800, when the Kingdom of Ireland joined the Kingdom of Great Britain.
"That it be the First Article of the Union of the kingdoms of Great Britain and Ireland, that the said kingdoms of Great Britain and Ireland shall, upon the first day of January which shall be in the year of our Lord one thousand eight hundred and one, and for ever after, be united into one kingdom, by the name of the United Kingdom of Great Britain and Ireland, and that the royal stile and titles appertaining to the imperial crown of the said United Kingdom and its dependencies, and also the ensigns, armorial flags and banners thereof, shall be such as his Majesty, by his royal proclamation under the Great Seal of the United Kingdom, shall be pleased to appoint." from the Union with Ireland Act 1800
The Kingdom of Great Britain itself only came into being in 1707 following the Act of Union, that is the political union. Before that from 1603 when James VI of Scotland inherited the crown of England through his grandmother being the sister of Henry VIII, it was a personal Union of the Crowns of England and Scotland. They were still known as the Kingdom of England and Kingdom of Scotland. This is why both King James are known by both their regnal numbers; James I of England and VI of Scots and James II of England and VII of Scots.
"The Two Kingdoms of Scotland and England shall upon the first day of May next  ensuing the date hereof and forever after be United into One Kingdom by the Name of Great Britain. And that the Ensigns Armorial of the said United Kingdom be such as Her Majesty shall appoint and the Crossed of St. Andrew and St. George be conjoined in such a manner as Her Majesty shall think fit and used in all Flags, Banners, Standards and Ensigns both at Sea and Land" from the Act of Union 1707
So as always the SNP a forgetting that there three crowns, or parts thereof that pledge fealty to their crowns, the term United Kingdom did come about as as aspect of the political union, not just the Parliament of (then) Great Britain. Those two are actually entwined in legislation. The Parliament of Scotland could in effect remove the protestant inheritance rights from the Princess Sophia Electress and Dowager Duchess of Hanover.
They actually are by wanting to tear up the Act of Union tearing up the United Kingdom. Her Majesty would therefore, if they were successful, become Queen Elizabeth II of England and Northern Ireland and I of Scots as she would return to being Queen of England and loyal parts of Ireland one one hand and Queen of Scots of the other.