We use our 'squishy debt' as our emergency fund.
Some of our mortgage is set up to act like a giant overdraft, whose limit decreases by a set amount each month - basically a standing line of credit on our house. Because we are aggressively paying down the principal, we have a huge buffer between our actual balance and the lending limit.
This works for me in terms of 'getting excited about it', because ANY money we have in that account is working, by reducing the interest to pay on the mortgage.
Without access to a house, any low-interest credit option could work - for amounts that you could readily pay off before the debt stops being low interest.
OR, you could put some larger amounts into some sort of term deposit. I have no idea about the rates available to you, but 3 amounts put into staggered 3-month deposits would give you access to 1/3 of your emergency fund each month at a (probably) higher interest rate than a standard savings account. You could cover any immediate emergency on a credit card and plan to draw down the emergency money within the month so the CC isn't carrying a balance.