The only time I wouldn'y allow a player to Delay after Aiming is if they wanted to Aim in preparation for an enemy arriving, since that's what Overwatch is for.

What we play, that seems to work well is the following:-

*Delay as written, so it's a half action on your turn to then have a half action before your next action (so that it can be higher up the initative next turn if need be) based on a condition.

*Aim can be used in previous turns and then used with the delayed action (as long as it is a shot, of course), assuming that no other actions have got in the way (like reactions)

*When performing the delayed action, it's an opposed agility check against the target to see who gets to do their action first (sadly can't remember if there is actually a rule for this or if it's a house rule). This makes delay worse than overwatch as it's both a half action, not a full (so you can't shoot as much) and overwatch is an automatic interrupt, not a challenge.

*Players are free to drop their initative at any point to a lower value, but obviously have to stick with this new value for the rest of the combat. If they do this then they are free to do a full action at the new initiative (which stops the "why are slower character get an advantage" thing). I believe this is a house rule, but I might be wrong.

To the original question, personally, I'd just agree with the players what interpretation of the rules makes most sense to everyone and just go with that (remembering of course, if they can do it then so can the NPCs).