I used to use the external mics I have couple of them but not using them anymore after I was told that the my voice from those was not very clear. If you want you can take one from me to try. They are comfortable, you put the Radio on your waist belt on the side and fix the mic on your shirt collar and more comfortable to work with.
These days I just keep them in the cup holders and pick up whenever I need to announce something.
But at the end buddy you are overthinking about it. There is no split second urgencies that need to be declared. You can take a second or two to collect the radio from the cup holder and announce.
Also driving with one hand is not as bad as you think it is. For me I tend to over stear when driving with both hands, and on high speed technical drives - especially the ones you mentioned with @Kailas I drive with just my right hand, holding on to the A pillar handle with my left hand on my Jeep.