If you need to buy time to build walls, look for spots to build forts in the incoming path (choke points, if possible) and dump a sacrifice unit in the fort. Each fort can usually slow the incoming by two turns unless the army has good siege gear. A couple of those serially and you have your four turns. When desperate, I save some fractional units for this duty. A few men to put up a bit of a fight, slingers or archers of some sort will kill more than their own number, doesn't hurt to take a small bite out of the stack too.

I find playing EB I have a LOT more battle losses due to delaying tactics like this. No general is involved with the fort cases, but my HA delayers usually have a general and I don't see many negative traits (though I have seem some damage to morale in a case where the general in question was very young).