Depends on the number of inputs/outputs and script type. But yea, it's independent of amount. Use the calculator.

So, this means that if I transfer 1 BTC to my Cold Wallet, it would cost me only 960 Sats? 

IamSINGLE

Radentor

Given a tx with 1 input and 1 output, onchain size would be 192 vbytes.

192 vbytes x 5 sats/vbyte = 960 sats = 65 cents at $68k/btc

bitcoin_beginners

Why Are On Chain Transaction  Fees So Low Now?

siggy47

Given a tx with 1 input and 1 output, onchain size would be 192 vbytes. 

192 vbytes x 5 sats/vbyte = 960 sats = 65 cents at $68k/btc

https://bitcoinops.org/en/tools/calc-size/