Necro for interest.
If you dip two levels (6 and 7)
So you already have the free improved critical into urban barbarian you get a + 2 to hit and + 2 damage from your controlled rage. The +2 damage you would get from precise strike anyway and 2 levels lets you rage for only ~7 rounds max. Low level rage powers don't really add to a swashbuckler at first sight except maybe reckless abonden if you plan to parry and reposte the next attack anyway. Unlike a rogue a swashbuckler doesn't really benefit from natural weapons so in total; I think it isn't really an improvement in combat. Roleplaying wise raging pirate gnomes sound pretty sweet ;)
In Soviet Pathfinder, Swashbuckler is good dip for you!
Seriously, a 1-level dip in Swashbuckler does a hell of a lot more for an Urban Barbarian than the reverse. The Urban/Invuln Barb is a significantly better chassis for a character than the Swashbuckler and many of its goodies come at later levels; it's feat starved, though, which an Inspired Blade dip really helps with.
The Swashbuckler dipping Barb loses out on precise strike advancement and only gets a few rounds of what is one of the best martial self-buffs in the game... once you have enough of it that it lasts forever. The dip is definitely not worth it.
Also, no alchemist is probably not that good, if only because the +DEX mutagen also lowers your wisdom, and thus your will save.
That, plus the fact that it takes 1 hour to make and would only last 10-20 minutes as a dip means it is probably not worth it for the mutagen (you might like some spells though; might be nice for a inspired blade with some INT).
Combined with the fact it is 3/4 BAB, you are losing 1 attack and damage all the time in return for gaining 1 attack and damage above a pure swashbuckler for a very limited time at a steep price. You also gain a bit of natural armor, but overall, it is not a good price.
Multiclass swashbuckler/monk can be interesting, percision flurry
Although you would want either to take monk to level 4 (ki pool, and thus extra attacks by spending ki) or level 8 (flurry adds in improved TWF). Just getting 1 extra attack might not be worth it.
Also- take the sohei archetype. It allows you to use light armor. Thus it is more friendly to the swashbuckler's AC since it has to deal with how AC bonuses from the classes scale; remember, mithral breast plate counts as light armor for restrictions other than proficiency, and armor expert removes the penalties of non-proficient use; that +6 is more than you will get from the monk dip.
Sohei can flurry with daggers (I know everyone is crazy for slashing grace, but these two classes are the best at using agile weapons since they only need 1 for their attacks, and they they can afford the price to save a feat). Combine that with the fact that it gets weapon training at level 6 (a nice +1 to attack and damage, and qualifies you for dueling gloves for an extra +2 on top of that) and you can get some decent damage.