Yeah, that's a nice idea...
If you manage to recharge simple "non-rechargable" AA or 9V batteries
using a Bedini charger, that would be cool
Would a relatively simple setup of a voltage sensor and a switch (transistor) work?

On a different note, did you guys know that the 9V "block" batteries are
actually 6 small cylindrical cells wired in series? Or at least, the alkaline
"non rechargable" ones are. I have opened up several different brands and
they were all the same: 6 thin zinc cylinders with a carbon filling and a
goopy sludge in between, the electrode on the carbon a simple metal
nail of about 3 to 4 mm long, isolated from the zinc by a thin layer of plastic.
It's similar to some large 12V battery blocks, as some brands appear to
fill those with a number of standard AA sized batteries in series...
Back in school they taught me that block batteries are the only ones
that actually contain a row of dissimilar metal plates in an electrolyte solution,
which was the reason why they put out a higher voltage. Although wiring
6 or more cylindrical batteries in series does effectively give a similar setup,
I do feel a little bit cheated by the battery manufacturers...

you can buy a 'proper' charger for alkaline batteries, the one below is about ?25 (one of the
more expensive ones) but they can be quite cheap. they've been out for a few years.
heres a snippet from the website :-

The EverCharge Multi-Function Multi-Chemistry Universal Battery Charger represents the latest innovation in battery charging technology. Not only does the EverCharge perform quick charging capabilities to Ni-Cad, Ni-MH, and RAM batteries, but it also can safely recharge previously non-rechargeable Alkaline batteries.

The ability to recharge Alkaline batteries will not only save you money, but it can go a long way to helping the environment at the same time. With over an estimated 30,000 tonnes of used batteries, classified as hazardous waste, being deposited into our landfill sites every year in the UK alone, the EverCharge is an important Eco-Friendly product.

Recharging of Alkaline batteries is dependent on the quality of the battery but tests show that the alkaline batteries can be recharged up to 85%-90% of their original capacity up to 15 recharges and costs literally pennies to recharge. This makes the cost of your standard batteries almost a steal.