If you really want to keep this shitcoin: create a good old paper wallet with a legacy Bitcoin address. Don't use any of the scam websites, you could just use Bitcoin Core or Electrum to create a legacy Bitcoin address. Back it up, and send your BSV there.
That takes the rush out of your January deadline.

I see no point in keeping this currency, as it is removed from many central exchanges and liquidity decreases, which makes withdrawing it to any wallet and reselling it again difficult due to the lack of platforms that list it.

If you prefer an open source wallet, there it is electrumsv
If you prefer a closed source wallet, there it is Trust wallet
Coinomi development was stopped more than a year ago. The wallet is closed source and there may be security problems. It is best to delete it and transfer your currencies to a new wallet.

Coinomi is the best choice for BSV and I don't get what you mean by they don't work? Can you elaborate about not working part...

I found an interesting wallet called ElectrumSV and looks like exact replica of Electrum and claims to be open source, so you can try that and it may work.

Github: https://github.com/electrumsv/electrumsv

Download here: https://electrumsv.io/download.html