Actually, yes, there is a way to do so without restarting Pulseaudio:
pacmd unload-module module-udev-detect && pacmd load-module module-udev-detect
I use it everytime I plug in my external-soundcard or after waking up my laptop. Pulseaudio cleans up his room and bring back my Spotify music on my external soundcard automatically (as it is my default soundcard).
You will need pacmd
to do so; it is included in the pulseaudio-utils
package on Ubuntu.