I rigged up last night.  Being winter, I rigged up an UL c-rig. I used a tiny barrel swivel.   I’ll toss it around for panfish if I get bored or the bass are reluctant. 
 

got me thinking. (O-0h!). What if I thread a sinker and instead of tying on a swivel, I thread on a bobber stop (or two if the sinker is heavy)and then a hook at the end?  That way I can adjust how long my “leader” is and I reduce the knot ties!  (Time save)

 

Is the swivel crucial to the c-rig?

No, in fact Carolina Keepers are a sort of modified bobber stop. 

 

That set up you are describing with a sparsely tied gnat fly is my preferred panfish rig. 

For a really light rig, you could just make it a Mojo (split shot) rig however you like it.  In fact, I think that you might be in effect doing that.  If you put bobber stops on a barrel or other cylindrical weight, it will make the rig less cumbersome to put together than a Carolina rig, but you don't have to crimp the weight on small line (which worries me).  You will lose one of the major benefits of the Carolina rig - the fish doesn't immediately feel weight when it picks up the bait.  Ultralight gear isn't what I think of when I think Carolina rig anyway for a couple of reasons.  1) If the leader is any lenght at all, it's not the easiest hookset, especially if the rod is short.  2) Generally people want the weight staying on the  bottom, and with any current or depth, the UL weight rating can be exceeded.  That said, I must be one of the last fans of the Mojo and Carolina rigs.

Can I rig up a heavier setup like this.?  12lb flouro?   0.5 oz weight?   More traditional c-rig like?

You'll probably need more bobber stops than is ideal. 

 

If that's your desired set up then step up to Carolina Keepers. Although I will say that personally I don't like them as my line typically breaks at the Keeper vs the hook.

 

1 hour ago, CountryboyinDC said:

That said, I must be one of the last fans of the Mojo and Carolina rigs.

Me too!

1 hour ago, They call me “Gaiter Salad” said:

Can I rig up a heavier setup like this.?  12lb flouro?   0.5 oz weight?   More traditional c-rig like?

I guess you could, that's definitely not UL, although I may have misread your intentions in the original post.  If you're only putting a stop between the weight and the hook, @garroyo130 is probably right, it will take more than one to keep it from sliding back.  If you peg it, put a stop on either side of the weight, 1 or 2 may hold.  1/2 oz is more than I've ever rigged that way.

I use 1 ounce weights for Carolina fishing and bobber stops or Carolina keepers do not work, I tried them . Maybe if I used several they would hold .

In my experience, the benefit of the swivel is that I can swing pretty hard on the cast to maximize the distance.  With a Carolina Keeper, I need to do a gentle lobbing action or the keeper will slide and shorten my leader.

I do this in the dog days when I can't buy a bite. I use an 1/8-3/16 oz. bullet weight and a T rigged 4" Zoom finesse worm or lizard. I had a day this past summer where the lizard saved my day. The bobber stop gives you infinite adjustability of the leader length. Since I use braid on both my bass spinning combos, I'll use about a 4' leader of low vis 10 lb mono. The mono is plenty long enough for the entire C rig. I call it my Finesse C rig. Very similar to a split shot rig except the weight is not fixed.

1 hour ago, Chris at Tech said:

In my experience, the benefit of the swivel is that I can swing pretty hard on the cast to maximize the distance.  With a Carolina Keeper, I need to do a gentle lobbing action or the keeper will slide and shorten my leader.

Use 2 Carolina Keepers when 1 won't suffice. 

4 hours ago, scaleface said:

I use 1 ounce weights for Carolina fishing and bobber stops or Carolina keepers do not work, I tried them . Maybe if I used several they would hold .

I've used two successfully before with heavy weights.

When bank fishing in the south, I've often used cactus spikes to pin a bullet weight in place for Carolina rigs.  Sometimes, I've also used toothpicks or whittled down twigs.  Just whatever I have handy.  It allows me to switch between Carolina and Texas rigs and adjust the leader length with ease.  

They make a product called a bull shot. It’s a bullet weight that crimps on like a split shot. No need for the bobber stops or keepers 

1 minute ago, TnRiver46 said:

They make a product called a bull shot. It’s a bullet weight that crimps on like a split shot. No need for the bobber stops or keepers 

Ya - if they don't get shut down...again. Water Gremlin keeps getting dinged for violating pollution standards at it's plant.

 

They're local (same metro area) as me.

I have never used a bobber stop myself for a Carolina rig but I have multiple times read/heard of people doing so.