Choosing 'You each lose a String on one another' if you have no Strings?

[Cneph]

So, Randolph the vampire is acting aloof and unobtainable after class, Shutting Down Valerie who is in a roundabout way trying to ask if he's already got a date for the Spring Formal.  He has no Strings on Valerie, Valerie has one on him.  In absence of other modifiers, if Randolph rolls a 7-9, can he choose 'you each lose a String on one another'?  In this case, only Valerie has a String to lose.  Or, does he have to pick that they exchange Conditions, like 'Dateless and Desperate' and 'Smug Prick'?

[mcdaldno]

Yes, you can still pick that, and if only one party has Strings, one party loses Strings.