I don't think the OP is saying they don't have a verified bank account on file - they may or may not, but if they don't, the transfer is likely to take a bit more than 3-5 days because the account would need to be verified first, then funds transferred. (You can also withdraw funds without having a verified account - a verified account give PP authorisation to debit an account, you don't need to give them that permission to send PP funds to one). 

If your PP balance is too low, the refund can't be done no matter what other funding sources you have on file, and the only way to get an instant credit is to receive an instant payment (I think it may be possible to add funds to your account via credit card, but I'm not 100% sure, otherwise you'll either have to transfer the funds by bank deposit, or if you're desperate, get someone with a credit card to send the funds to your account as a gift, fees are charged on those types of payments, so make sure you cover all costs etc 😉 ). 

That's in general, anyway, as I agree a no-questions-asked refund is not necessarily the best idea.