After viewing a variety of shuttle options, it strikes me that a taxi from the 6th arrondissement to Orly might be both more convenient and cheaper. Am I missing something here or on the right track? Any reason not to have the arrangement made by my hotel's concierge?

Not cheaper but more convenient. You can take the métro to the RER B which goes to Antony where you would transfer to the Orlyval shuttle.

Do you mean have your concierge call you a taxi or do you mean have the concierge arrange a shuttle? Either way, sounds like a good idea, I don't know what else you would do about the taxi, in any case. YOu might be able to arrange a shuttle cheaper than the one your hotel uses, who knows.

Some people will likely tell you that you can save couple euros if you don't have your hotel call a taxi but you go yourself in search of a taxi stand (because they can charge from the point they leave to get you, there will be a small charge on the meter at pickup). good luck with that one, if you decide not to have your hotel arrange a taxi. I would never risk it to get to the airport, unless you know for a fact that there is a taxi stand right near your hotel and you've observed it enough to know you can easily get one there without waiting, at the time and day you want.

I always let my hotel make arrangements for me (taxi or shuttle) as I would presume the companies want to keep their business and they have experience with whom to call for the best service. I'd take a taxi rather than shuttle to Orly.

We took a taxi.Easy peasy!Glad we did...because the line to check into our flight was enormous!!
Tina

Just bear in mind that in Paris the taxi meter STARTS when the wheels begin rolling and NOT when the taxi arrives at your hotel.

Taxi fare to ORY is about half of what it is to CDG (about 25€ to 30€). You will not find any private shuttle anywhere near that inexpensive. The metro/train option via Antony will cost near 10.90€.

There is also a city bus that goes from Denfert-Rochereau to Orly.

Sarastro +1
Shuttle is not the best option from Orly.
Taxi shouldn't cost more.

You can easily call or text for a taxi yourself:

http://www.taxis-bleus.com/

A taxi is the way to go if you prefer to snub public transportation.