Usually less SLS would be required than SLSA.
However, I would not be put off from using cocamide DEA (coconut diethanolamide). The "possible carcinogen" was a total fluke result in some screening in rodents that I as a cancer researcher would not give credence to. There are other reasons to prefer other ingredients to fatty diethanolamides -- various substitutes are lower in eye sting and skin irritation, and waterlog skin less -- but in some applications like bubble bars cocamide DEA may still be the best choice.
These fatty diethanolamides serve as foam stabilizers, and allow you to use much less primary foaming agent (SLS or SLSA or other) than otherwise. So even though the fatty diethanolamides are much more irritating than most surfactants on a mass basis, in actual use they're reducing the total surfactant concentration and thus irritancy in the product overall. In a liquid product there are other foam stabilizers that are milder still, but cocamide DEA is very convenient to mix into a solid product, expecially a tablet, in the amounts useful in such a product. It is possible, though not as easy, to make a tablet with other foam stabilizers that come in water solution, such as alkamidoproyl betaines, and if you're making a combination fizzie-foamy it's practically impossible to be using that much water. (I don't recommend combination fizzie-foamy tablets, but they're in common use.)
Without the cocamide DEA, you'll need more SLS or SLSA to make the foam last as long, and then you're getting a "soapier" bath than you might want; you want the bath to have foam on top to be played with, not to be detergent enough to do laundry! A typical formula would use a weight ratio of, say, 8:1 of the anionic surfactant to the cocamide DEA.