Swan chairs with dried out foam padding  

If the foam is that bad, the fabric
may be worn enough that it's not worth the savings to reuse it, even if it's possible. It may have only another 5-10 years of wear in it, and then you're looking at a total re-do.
Anyway, no, you can't open a seam and stick new foam in. All the fabric has to come off and the foam must be completely scraped off the hard shell. Then new latex foam is glued on with the right thicknesses in the right areas. Then the new fabric is glued to the foam and the seam around the perimeter is hand stitched with the stitches being of a specific length.
I think BK Upholstery in PA is considered to be a reputable restorer of these chairs, and they publish their rates on their site.
Good luck!

Thanks.sound like you've...
Thanks.sound like you've been there, done that.

You need to have them reupholstered
If cost is your primary concern, you need to just have them reupholstered and replace the old fabric with new fabric or leather of your choosing. You can have the old fabric removed and cleaned, the foam replaced, and the old fabric put back on, however this will cost you more in additional labor than it likely would to replace the fabric with new upholstery.
I know, I just had one done. I got an amazing very early swan chair in incredible condition, except for the petrified foam. If the fabric had not been so wonderful and my desire to restore the chair to original so great, I would have just selected a new fabric or leather and had it redone. It would have been less expensive. But I chose to try and have the chair restored, which meant that the old fabric had to be painstakingly removed taking care not to rip or tear it. The fabric then had to be hand cleaned, making sure to remove all the old dried foam that was stuck to the back. The shell was then stripped down and new foam was applied (this is one of the expensive parts of doing a swan or an egg; the foam should be sculpted to the varying thicknesses. The foam is not one uniform thickness as it was originally created with a mould and is thinner in some areas like the arms and thicker in the seat, headrest, etc.). The original fabric was then reapplied and hand sewn, they even took care to sew it through the original holes making sure the seam fell in the exact original place.
All of this took more time and care than simply having the chair reupholstered (still a time and labor intensive project compared to other chairs) so it cost a bit more to do. The result however, was well worth the cost to me as I ended up with an amazing museum-worthy example of the swan.
If you decide to redo your chairs (and I think it would be well worth doing), I would be very careful selecting a shop to have them upholstered. I have seen many, many swan and egg chairs that missed the mark when they were reupholstered. I would ask for referrals from others who have had the work done, I'd want to see examples of their quality, and to know that they understand how the chair is supposed to look when properly reupholstered. I could recommend a couple of folks who could do it correctly, but they are in Chicago and it would involve you shipping your chairs to and from.

Thanks.
Thanks so much for taking the time to explain your experiences with your swan chair. I've gone online to check out the firm in PA that actually is licenced to make the chairs for Fritz Hansen. I will continue to search for a fim closer to NYC so that I can visit them and also save hundreds on shipping. I'd rather put the money into workmanship and fabric than into shipping. If anyone knows of upholsterers in NY or NJ that are up to the task, please post their names. Thanks again.