Shortly after writing this I saw that the whaleshares tokens were being offered to be bought back after a whale removed their delegation to the project. So I'd first check that the project is going.
But yes, you'll need the bitshsares wallet (openledger i believe) to be able to buy and hold them. It's been a long time since I'd gone through that, so I would suggest asking one of the people on that discord for instructions. I'll reply a guide if I find one that looks to be well written. (I don't think I have one together for that right now.)
Thank you very much!