The Hamster Kombat ($HMSTR) withdrawal process is generally tied to The Open Network (TON) blockchain, and most withdrawal paths lead to a wallet or exchange that supports TON.

However, your intention to use Minimal KYC and potentially avoid TON fees can be addressed through the Centralized Exchange (CEX) withdrawal option offered by the game.

Here is a breakdown of the transfer process, focusing on the options that meet your criteria:

1. Minimal KYC Option: Withdrawal to a Centralized Exchange (CEX)
The most efficient way to convert your $HMSTR to tradeable currency is by sending them directly to a major crypto exchange. This method often bypasses the need for you to buy TON for gas fees, but it does require some level of KYC on the exchange.

Major exchanges (like Binance, Bybit, or OKX) were official partners and offered direct withdrawal options from the Hamster Kombat bot.

Steps:

Select an Exchange: Open an account on a major exchange that supports the $HMSTR token (e.g., Binance, Bybit, OKX).

Check KYC Level: You will need to complete the exchange's minimum KYC requirements (usually name, date of birth, and email verification) to deposit and trade. Full KYC (with ID proof) is often required for larger withdrawals or cashing out to fiat currency (bank account).

Find Deposit Details: In your chosen exchange, go to the Deposit section, search for HMSTR, and select the TON network.

Crucially, copy the:

Deposit Address

Memo / Tag (This is essential! Without it, your tokens can be lost.)

Initiate Transfer from Hamster Kombat:

Open the Hamster Kombat bot in Telegram.

Go to the Airdrop or Withdrawal tab.

Select the withdrawal option for your chosen exchange.

Paste the Deposit Address and Memo/Tag you copied from the exchange.

Confirm the transfer.

Why this meets your request:

Minimal TON Needed: Transfers to major exchange wallets (CEX) often have fees covered or zero fees during the initial distribution period. The exchange handles the on-chain complexity.

Minimal KYC: Basic KYC on the exchange is usually enough for deposits and small trades, but full KYC is needed to withdraw large amounts or cash out to a bank.

2. The Telegram Wallet Option (Requires TON for Final Transfer)
While you can receive your airdrop into the built-in Telegram Wallet, moving the tokens out of that wallet to a liquid exchange for selling will require a small amount of TON to cover the network transaction (gas) fee.

Steps:

Connect Telegram Wallet: In the Hamster Kombat Airdrop/Withdrawal tab, link your Telegram Wallet.

Receive $HMSTR: The tokens are distributed to this wallet after the Token Generation Event (TGE).

Transfer to an Exchange (The TON Requirement):

To sell the tokens, you must send them to an exchange (like in the first option).

Go to your Telegram Wallet and initiate a "Send" transaction for $HMSTR.

You will be prompted to pay a small gas fee in TON Coin.

You must buy a small amount of TON on an exchange and send it to your Telegram Wallet first.

Why this partially meets your request:

Minimal KYC: The Telegram Wallet itself has very low KYC requirements.

No TON Needed (to receive): You receive the tokens for free.

TON IS Needed (to sell/transfer out): You cannot move the tokens out of the wallet without a small amount of TON for the transaction fee.

Disclaimer: Always ensure you are following the official, updated instructions from the Hamster Kombat official Telegram channel or website to avoid scams and loss of funds. The token distribution and withdrawal process can change.