The spring hanger itself is worn beyond serviceability, because the eyelet has been eaten through on the top, as seen in your first photo. The sides of the hanger is worn out of round on both sides from the shackle being driven around for a long time loose, or repaired previously incorrectly. Not to worry, this isn't a huge deal to fix, and to answer your question, you can use the later closed shackles, as long as you use the correct bushings in the hanger and spring. You can do one of three different fixes;

Replace the spring hanger completely: https://www.kaiserwillys.com/product...71-cj-5-m38a1/

Retain your current spring hanger and cut out the remainder of the sleeve, and go with the heavier duty closed shackle: https://www.kaiserwillys.com/product...non-greasable/

Or, if you want the look of the original 'C' shackle but want a bit more durability, go with the M38A1 shackle: https://www.kaiserwillys.com/product...8a1-greasable/

I personally would go with the M38A1 style, because I like the originality of the 'C' shackle because they are greaseable for a longer life of the repair. The downside to this for your application, is that you would have to replace the eyelet with the threaded bushing.