There are 2 main alternative methods you can make use of to get the balance of the wallet. To start with, if you have the seed phrase or private keys to the wallet you can access the wallet via the keys and proceed to going through the transaction history and balances of the wallet.
Like I said up there with the OP definitely saying he has the address then to me there is no need for the seed phrase or private key. The keys will even require him to prephend to the actual and address also adding the security implications on importing seed phrase and private keys then OP should just import the particular address on any of the wallet or explorer.
It's always better for privacy if you check your address balance, wallet balance with your own wallet. Better with VPN or Tor connection and your full node.
When you check your address with block explorers, you depend on their care on your data and privacy, so it's not recommended.
When you check your address with block explorers, you depend on their care on your data and privacy, so it's not recommended.
There is no better privacy than using your own full node as you said. But we all know that it comes with the conditions of having to download and store 500GB plus data now. For just address check I think that will be too much for the OP except he prefers to run the full node beyond today. My suggestion is for him to use SPV wallet like electrum suggested above to run this
