Responsibility for what? You purchased a (presumably cheap) Visby-ARN SAS ticket and the flight was delayed and now you expect SK to reimburse EUR 1,500 because you had a separate BA ticket to JNB? (and you even declined the offer of SAS to rebook you for the following day on BA). Seriously, I don't get why you expect SK to take more responsibility than SAS already did. SAS owes you nothing in this situation (and I'm surprised that apparently SAS was even prepared to rebook you for a flight the following day as there was no duty to do so).

Contact your travel insurance for reimbursement of expenses incurred to buy the TK ticket. If no insurance coverage, there is nothing to do than to file this under "lesson learned" expenses.