Is it the definite consensus that there are NO OPTIONS to get the SV without updating firmware? Because yes, the Ledger is empty, so no risk at this point.
You can wait for more answers to your question, but I think there is no other way to go claim BSV from hardware wallet without seed and without BSV app+ElectrumSV as described in the procedure on the Ledger page.
There is a risk, but also a pretty good chance that the Nano S won't reset during firmware update. It just takes patience and some time since you have very old firmware, but it can be done successfully.
Even with the latest firmware 1.5.5 every user of Nano S may experience a reset during regular use, there is some bug that should be resolved in the next firmware (hopefully by the end of this year).