That's great you have some S-23, it's a great yeast. Just be wise about choosing your style: S-23 is a pretty estery yeast as far as Lager yeasts go (no comparison to the Ale yeast ester levels though), so a German or Scandinavian Lager brewed with S-23 most likely will come out as a faulty one (hence the bad rap S-23 gets in the interwebs). S-23 is ideal not for German but for Austrian, Czech and Polish Lagers which are traditionally a bit more estery than German. Brew a Wiener, a Budweiser or a Zywiec with it (I'm not touching the subject of Porter Baltycki or Boehmisches Dunkles, as we're talking about light beers now). With those styles, you'll be spot on.
If you are set on making a split batch - a decocted one and an infused one - I'd suggest mashing them in separately and simultaneously. I've done that, it's not too hard to do. Well, you could mash them in both together at 38C or 55C, but then you'll have to split them equally for the decoction anyway, which will bring an added hassle. What I did, was mashing my grains in simultaneously in two mashtuns and keeping the infusion mash steps' lengths equal to the time it took the decoction part to be heated and boiled. As a result, I got some unusually long step rests for my infusion mash part (like 1 hour at 55C, 1.30 hour at 62C etc.) but this aspect is known and discussed in German brewing literature, the common thinking is that it's OK.
I would say I tasted a tangible difference between my split batches, that's why I'm a strong believer in the virtues of the good old decoction. You may find people that deny the difference, some of them well-experienced brewers, but I believe most of them probably have never tried a split batch.