The DPIs that are legally required to be disclose are set out here:
What you describe would not be a DPI as you gain no personal benefit from your position. They relate to gains not losses. So if you are only liable for losses that is not a DPI.
Sensitive interests are interests that could possibly lead to you being subject to violence or intimidation if they were revealed. On agreement with the Monitoring Officer the nature of these interests don't have to be revealed (but you do still need to declare that an interest exists).
It is a criminal offence not to declare DPIs. No standing order can override criminal law.
Don't forget that under your Councillor Code of Conduct you do also need to declare 'other registrable interests', and being a trustee would be one of these.