To get back to the original question: I don't think the OP cares whether the shoes pictured are shell. I think that is just a photo of cracked shoes that he found, and used to illustrate his question. He wants to know how to preserve his shell shoes that are NOT cracked.
From discussions here and on AAAC, I have seen the following responses, as best I understood them. Note, I cite several individuals, but it is possible I misunderstood what they said. So don't blame them if I got it wrong:
Shell is so heavily saturated with waxes and oils when it is made that no further treatment is needed, or even possible.
Shell is so dense that nothing will soak into it, no matter what you might apply.
Shell dries out like any other leather, and must be conditioned the same way. Wide variety of favorite conditioners, but the cobbler who posts as Cobblestone and Nick Valenti of B Nelson both say they use Lexol. Nick V has also spoken highly of Saphir products. DWFII, boot and shoe maker, also says he uses Lexol, and specifically prefers LexolNF, which apparently soaks in quickly without leaving a residue. I have not seen comments on maintaining shell from Ron Rider or Calfknip, other experts who sometimes contribute their knowledge.
I think each has endorsed treating dry shell with Lexol, but it is possible any of them may have been referring only to calf, and I missed that point.
Some, not necessarily those above, have said that any shoes new to you, whether purchased used or new, should be conditioned. The argument goes that you have no idea how long the shoes may have sat without conditioning, the temperatures or humidity to which they were exposed...
Others have said that this is an issue only for old shell and that new shell will be fine for years without conditioning.
Nick Horween, whose company makes shell, has cautioned against using any conditioner with solvents. He suggests Venetian Shoe Cream. I think the only solvent in Lexol is water, which also appears to be in VSC, so I am not sure whether there are other reasons he is concerned about Lexol. For a while it sounded as if the Horween company was preparing to introduce their own conditioner, the same mix of fats and oils used in producing shell. Have not heard anything about that for a while, so I don't know where that stands.
VSC does not seem to penetrate deeply into shell in my experience (which is not that much). It gives a nice surface shine, but I don't know whether it does much conditioning.
I would love to hear from the experts about
The need for conditioning new shell
Need for conditioning old shell
What conditioner to use when necessary
How to distinguish shell that is simply dry, and can be saved by conditioning, from that that has undergone dry rot, and is beyond salvation.
I hope I have dropped enough names to attract their attention.