I'm not sure.
If someone wants to rob you, it probably doesn't matter whether you have the private key with you or a signed tx which shows how much money you own.
There are 2 cases:
1) If you have the private keys with you, he steals your money
2) If you don't but the burglar sees how much money you own, he might kidnap you if the amount is high enough. And if the amount is pretty low, well then losing this wouldn't matter at all and the whole setup wouldn't be required.
So in the end it might come down to what is more valuable to you: Your money or your health.
So, i'd say this question is not as easy to answer as you might think.
However, having a menmonic code with you, which is protected by a BIP39 passphrase might be a better option here.
The thief would take your mnemonic code and steal all the low amounts of BTC from the wallet. Without the password however, he will never access the large sum of BTC. You lose a little bit of money but don't get kidnapped.
Of course, your life is more important than your funds. No matter if it is private key or a signed tx, a robber would easily find out how much do you own and if he wants to take this from you... well there is not too much you can do.
Same applies to a BIP39 passphrase protected mnemonic code. He sees there are only a few bucks, takes or leaves them and you are free. He won't know how much you own. And you saved the majority of your funds.
With your approach.. if he sees the signed transaction, he knows how much money there is. Might be worth to kidnap someone.
Not sure how the BIP39 passphrase protected mnemonic code would not reveal your balance. Care to explain this? Thank you.