What sort of amount are we talking about here, and what countries are you travelling to?
As long as it's not cash, most countries will neither know or care how much money is in your bank account or on your credit card limit, and can't even check if they wanted to. Even if they can, there are very few countries where they would check without already suspecting you of a crime. I think you're worrying over nothing. Even if it's cash, most countries have no border control anyway, and those who do (UK, Ireland) allow up to £10,000 or so cash without even having to declare it...
Just open a second bank account and don't take the card (or cut the card up). Use online banking to transfer money in smaller chunks to your main account.
Alternately (or additionally) take a credit card or two with a smaller limit (enough to make sure you're comfortably able to deal with one month plus emergency money). Then set up your regular bank account to pay this credit card off in full every month.
If I was really concerned, I'd open a second bank account and add a sensible amount of money to it (enough to cover costs of my stay and avoid questions about whether I can afford my stay, but not so much it would raise question). Then I'd open two credit cards with a limit of perhaps $1000-2000: one covers the costs of living wherever I'm going, the other is for emergencies or if I misjudge and go over my amount per month. Set up your bank to pay these off each month, and you're sorted
Honestly, I think you're worrying over nothing. People travel inside Europe every day with millions in the bank and raise no questions. You're legally allowed to have money!