The cheapest way to wire back my SGD to Singapore without currency conversion.

I did something stupid.
Last time I went back to Singapore to cancel my inactive bank account and withdraw all my money.
I intended to put it back to my another Singapore account before coming back to Japan.

But I forgot about it and brought a pile of SGD cash to Japan.

Is there way to send this pile of cash back to Singapore with the minimum amount of processing fees?

I know I can simply convert SGD to JPY. Then save it into my Japanese bank account. Then wire it back to my Singapore bank account and convert it back to SGD. But there are just too many layers of processing fees.

by athrun200