To me, a concert is an opportunity to shape discussion. I want my audience to talk about context, the performance itself, or how they felt during the event but absolutely not about my equipment. As early musicians, we seem to get carried away often enough about what is historical or not: instrument, pitch, temperament, etc., and we shouldn't allow that to bleed into the concert itself as it only invites unwanted judgement and discussion.
For example, last year I went to go watch the Ottawa Bach Choir perform a concert of early 17th century music (I think it was German?) accompanied by a great group of 17th century instrumentalists (cornets, sackbuts, dulcian, violin, organ, harp, etc.) who styled themselves 'La Rose des Vents'. The concert was very well performed, but it bothered me that the conductor, while giving a brief introduction, included that the ensemble was playing at a=465 in Valotti temperament. I gave a big snort while the rest of the audience seemed to 'ooh' and 'aah' as if they were somehow in the know. For those of you who didn't get that last bit, the temperament came about many, many years after the music was shelved. My point is that had this conundrum not been mentioned, I would have no story to tell! I remember this OBC concert over all the others that I have attended because of this tiny historical hiccup.
These hiccups happen all the time, they will always be there as we aren't living in the 17th century, but we must choose to put the emphasis on the performance. The harder we grasp at being how some would say 'authentic', the slipperier that bar of soap becomes. Playing a 17th century violin? It's a copy. Got an original now? It's been modernized. Got that fixed? It's German so you should shy away from playing Italian music if you know what's good for you. However much you are concerned about these things - to a certain extent I am too - don't allow an opportunity for these kinds of judgements to occur in the concert for it will only distract and/or detract one from the experience you're engineering. The simplest way to do that it to eliminate the 'authenticity' discussion completely.
It is understandable that many who come to see an historical performance don't know very much about the equipment we are using but ask yourself if your event is principally for educational purposes or artistic. The most grueling thing for me to watch is an ad-libbed description of one's instrument. Yes, maybe the audience has a better understanding of how it works, but will knowing that you are playing on gut strings make the performance of the Messiah that much more uplifting? Even in extreme cases, like krumhorns, I think it would be best just to mention that you're available to discuss the instrument during the interval or at the end - it adds an element of personal discovery within those interested and there's more time for entertainment. I am still perplexed why some presume that I came because I want to hear a musician speak extempore. No, I came to hear you play.