First of all, ChipMixer have been operating for years, their forum account has 100% positive feedback (
https://bitcointalk.org/index.php?action=trust;u=1003345), and they have never scammed a single satoshi, so try not to worry too much.
If you have asked ChipMixer to send your funds to your own address, then you do not need to use the private keys. You just need to continue to wait and the transaction will process in due course.
If you want to change your mind and would rather make a transaction yourself right now, then you can take the private keys for your chips and import them in to a wallet of your choice (most people on this forum would recommend
Electrum), and then make a transaction from those private keys to your own address and broadcast it immediately. Note that if you do choose to do this, then there is an additional risk since you are copying raw private keys on to your own computer and so there is a potential for some malware to steal them. You should ensure your computer is clean and free from malware, and make sure you verify the Electrum download before using it:
[GUIDE] How to Safely Download and Verify Electrum [Guide]There is also the possibility that ChipMixer have already broadcast the transaction, but it is currently unconfirmed and waiting in the mempool to be mined. You will be able to tell this if you look up the address you are trying to receive coins to in a block explorer such as
https://mempool.space and see any incoming unconfirmed transactions.