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Given the selection mechanism, I'd be tempted to try a blind strategy. "I'm not going to look at my ball before I pick it, but if you split and I steal, I'll give you half the money."

It wouldn't be good against a pure money-maximiser, because his expected $value is higher for steal (1/2 versus (1+P(I'm honest))/4), but if he's risk-averse and trusting it might work out.

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It's not clear that this strategy is possible within the the framework of the game show though. The host instructs both players to look at the concealed choices before they're allowed to talk to each other. To employ the blind strategy you'd have to explicitly not look at them (and probably say something at that point to make it clear you don't plan on looking at them). This would be directly contradicting the host's instructions. While the host might allow it, I think it's more likely they'll say "sorry, but you have to look at them".

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