No, it has to be a bounty, otherwise the person attacked cannot legally defend themselves. It has to be a bounty and the attacker has to be wanted, the monetary part of the bounty is not important in that sense. I'm pretty sure that you'd be unimpressed if a player or NPC could start to attack you and you not be able to fight back until you had taken hull damage.
Babelfish's suggestion that bounties below 1000 credits could be paid off at the station is a potentially good one (I even
made it myself some time ago), although I suspect that it has the potential to create significant loopholes in stopping irritating behavior if there is no real deterrent.