is there any other way to check if the private key is valid to the pub adress without signing a transaction?

Use https://www.bitaddress.org offline. For offline usage, you can download the zip file from https://www.bitaddress.org/bitaddress.org-v3.3.0-SHA256-dec17c07685e1870960903d8f58090475b25af946fe95a734f88408cef4aa194.html to use on an airgapped device.

Click on wallet details -> enter your private key -> view details. You will see the compressed address. Check the address information on a blockchain explorer like https://mempool.space/ or https://www.blockchain.com/en/ to see the amount of bitcoin the address holds.