An independent Scotland in the EU would have the same border checks as the UK has. Border checks can be electronic, pretty seamless, and not physical whether in or out of the EU.
By the time Scotland becomes independent, the confusion over borders will have been cleared up and an independent Scotland in the EU would have the same border arrangement with the rest of the UK as the rest of the EU, but not be required to join the full Schengen Agreement. Scotland would also have access to the EU single market and that would lead to an exporting jobs boom.
If the UK cannot sort out its Brexit border chaos by independence day, then the UK economy will be in free fall and Scotland will need to escape the UK to avoid economic collapse.
Trading in sterling for a transitional period would mean goods from Scotland will avoid currency exchange issues, and if the UK doesn’t sort its borders then the subsequent fall in the value of sterling should mean that trade with the rest of the UK increases, not decreases, as Scotland will be the only nation from which rUK can afford to import. Where else would the rUK get the oil, electricity and food it needs from if it was cheaper and just as easy to import from the country next door?