I hate to say it, but I'd try to find a new domain if possible.
With domain hacks like this, They feel a bit dated, but worse, I never remember where the splits are.
Sec.ret.ly?
Se.cret.ly?
S.ecret.ly?
Also, how big is the use case? I don't think one load URLs are something I'd ever really want. What if they accidentily closed it?
And it doesn't prevent sharing, since they could just save it and re-upload..
Basically, either I trust them, or I don't. I don't see where a one-use URL helps.