Fact:
I refer to "A Complete Guide to Heraldry" by AC Fox-Davies page 475:
"James I on his great seal had the banners of Cadwallader (azure, a cross patte fitche or) and King Edgar (azure, a cross patonce, between four martlets or)"
In this instance we are obviously interested in that of Cadwallader - this is the device on the English Caldwell coat of arms and is there described as the "Cross Maltho de Caldwell".
James had been held captive in England for some time and married Joan of Beaufort. I presume that the devices on his seal were meant to allude to some great persons in his own ancestry from which he can draw the prestige of his own royalty.
Romance:
It is possible that his Stewart ancestors through the FitzAllans from Shropshire had married into the line of the legendry King Cadwallader of North Wales.
I might also raise the possibility that some of Cadwallader's descendents having become "Caldwell's" and lesser fuedal knights of the FitzAllan's came to Scotland with them.
Bigger Romance:
Other Cadwallader-Caldwell's retaining the association of the Cadwallader device have "morphed" it to the "Maltese Cross of Caldwell" along with the anglicisation of their Welsh name.
It is possible: Llewelyn ap Gruffydd would turn in his grave if he could hear the way modern day Llewellyn's pronounce their own surname in Australia! (very anglo-phonetically). As Scots born but 7 years childhood in Wales I can pronounce Welsh names - its not that hard once you know the basic rules.
As to the banner of King Edgar - which King Edgar - there was a Scots one and an English one. If it were the English one it would seem to signify a very tenuous connection with his wife's family and also an old enemy of the Scots which would not have been politically correct on his great seal. If it were the Scots King Edgar then it is worthy of note that he was the first son of Malcolm III and Margaret the Anglo-Saxon princess to rule Scotland (1097-1107). It was his younger brother David (1124-53) who is generally credited with bringing the Norman families to Scotland (including the FitzAllan's).
I am using the term "FitzAllan's" loosely here as at that time surnames had not been fixed. It is common knowledge that one of the FitzAllan families became the Stewards. It is not beyond conjecture that the family had married into the line of Cadwallader in the North Welsh Marches and had adopted his device. Cadwallader himself seems to have been much more revered by families through history than the recorded history of his exploits might seem to warrant. It is not just that he was a vigorous and for a time successful war-leader of a small kingdom under pressure. There were many others equally deserving of historical reverence. There was the connection of the Votadini and Mannau-Goddodin. He could even have been a role model for the famous Arthur - ... slap, slap ... oh horror don't start rambling off into a real argument Tom! (Good yarn though).
It is also very possible that the "King Edgar" referred to might even be Edgar Atheling the last nominal King of England and Margaret's brother - if this were the case it would amount to the same thing - a proxy (but enenforceable) claim to English territory.
If James wanted to show illustrious ancestors in his lineage he most probably chose to show Edgar as the fusion of Ancient Scots and Ancient English and the Ancient Welsh through his early Stewart connection to Cadwallader. Neat - gives him an allegorical claim to Kingship of all Britain!
Obviously been doing some thinking as well as courting Joan of Beaufort. (This is reputed to have been a love-match unlike many arranged royal marriages).
Please don't take all this as fact - I am listing this for debate and educated reasoning. If you agree and can provide more evidence to support these contentions then lets hear from you. If you disagree - please say so and let us know why.