However, you don't need to carry all those 10,000 with you all the time. You can send 9,000 to your HW and keep 1000 in a Electrum mobile wallet. Once the balance goes down, just move more to the mobile wallet.
This is the way to go 
It doesn't even have to be a hardware wallet, it could also be an offline Electrum installation.2. A hardware wallet (You can transact offline, you can transact using your mobile)
For the record: using a hardware wallet doens't mean it's offline. You could connect it to an offline Electrum installation, and sign the transaction on the hardware wallet, but that seems a bit excessive.Quote
Imagine, you have $10000 (in BTC)
Isn't it the same with fiat? I assume you don't keep all your money at the same place: some in cash in your wallet, some in your old sock or piggy bank at home, and some in the bank. You divide your money based on it's purpose.