Apart from lower current, and less wiring, are there any other significant advantages?
To be honest I'm not very concerned about the battery size, as the one I have weighs less than 500 grams, and will power a medium size motorbike horn (Although the smaller horn linked below may be better.)
All of my wiring will be in a saddle bag, apart from the horn which will be attached near the rear brake, and the switch which can be very small with thin wiring if I use a relay. A moped style horn, such as
this one, is quite small and very easy to mount.