No, definitely do NOT take that approach. You must provide the requested discovery unless you have valid grounds for opposing the request. Understand that discovery is very broad, anything that may be relevant evidence or that might lead to relevant evidence is generally fair game. When it comes to child support proceedings, pretty much all financial information about you is going to be fair game for discovery. Bank statements are clearly good for them to ask for. Credit card statements too. Why? Because what you buy and your payment of the cards can reveal information about your income and assets.
Don't just fail to provide the requested material. If you think you have a valid reason to oppose discovery, make your objection with the other party's attorney and try to work out the problem between you first. The Oregon rules require this step of conferring with the other side. If you can't reach agreement and your objection is based on confidentiality you may seek a protective order from the court. Otherwise, you need to be prepared to defend your objection when the other party files the motion to compel. You want to have at least a non frivolous objection to avoid the possibility that you might be sanctioned for the refusal to provide discovery as required by the rules.