I think metal detectors tend to pick up big stuff. The magnets on telescopic sticks are for little things like screws and filings.That's an excellent idea. There's always someone on the beach with their metal detector. Next time I see someone I'll ask them how much to do the yard.
I'll do the magnet sweep up too.
Bob mentioned the one you linked is a bit small at the end - even with the bigger ones it is a tedious exercise, I think the small one is setting you up for frustration.
Try and get a bigger one - I think Bob posted an example. If you cannot find one, you can work with the one you have got as long as you have a metal lid from a biscuit tin. If the magnet attaches to the biscuit tin lid, then the lid becomes your magnet to sweep the ground but with a bigger magnetic surface.
Of course a bigger magnet would still be better and you can get an even bigger biscuit tin lid!