May an easy example will help to explain this further and to figue out if my assumptions are wrong or not.
I'll make up an example for all 3 scenarios, and I'll rewrite your questions a bit.
1. Withdraw from CHP with Import Private Key in Electrum --> Spent the coins.
Let's say I deposited 0.02347273 BTC to ChipMixer on January 1, 2021. I got a 0.023 BTC voucher. Yesterday, I deposited 0.00482361 BTC to ChipMixer and added my voucher. I withdrew a 0.008 BTC chip, and got a voucher (0.019 BTC) for the rest.
Today, I start up
Tails OS (which connects through Tor), import the 0.008 BTC chip into Electrum, and spend the coins. I make sure to spend the full amount, without creating a change address.
2. Withdraw from CHP with Import Private Key in Electrum --> Sweeping in Electrum --> Spent The coins.
I shortened the question a bit: there's no need to import private keys if you're sweeping them.
Tomorrow, I'm going to use my voucher on ChipMixer, and withdraw a 0.002 BTC and 0.004 BTC chip. I take a voucher (0.013 BTC) for the rest.
I import both private keys in my normal Electrum installation (which I already have on my PC). I click Wallet > Private Keys > Sweep, and enter both private keys. After the transaction fee, I receive 0.00599617 BTC on the next unused Bitcoin address in my Electrum wallet. I use the Coins tab, select this input, right-click my mouse and click Spend. I spend 0.00456817 BTC and receive 0.00142685 BTC on a change address. I go to the Addresses tab, and Label the address: "CHANGE from CHIP, do not mix". Then, to avoid sending it accidentally, I click right-mouse and select Freeze.
This is slightly less anonymous than #1, but still pretty good, as it won't link any of my Bitcoin addresses on-chain. But the Electrum server I'm connecting to knows all the addresses in my wallet. If it keeps logs, my anonymity could be compromised.
3. Sweeping directly from CHP to an Wallet --> Spent the coins.
This is basically the scenario (#2) above. The level of anonymity will largely depend on the wallet you use: if you use an Android wallet from your home IP address, it's likely
someone can link your addresses together. If you use a web wallet for all your Bitcoin transactions, it's even worse.
I think #1 is the most anonymous method if you're limited to Electrum. You could probably do a bit better if you use your own Bitcoin Core wallet on Tor, but that is more work.