In this case (where you have the private key of the recipient of the stuck transaction), you can use 'Child Pays for Parent', i.e. you simply spend the unconfirmed output (to yourself) with a high fee. To get the high fee of the child transaction, the miner must include the parent transaction. No RBF is needed.
Okay so specifically as the receiver you can do this. Neat.
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One issue you could face with this method for your specific case (withdraw from exchange) is if the exchange withdraw transaction is very large in terms of vBytes (contains many other withdraws to other customers), it could be very expensive to do child pays for parent because you are having to pay for everyone's withdraws to confirm, not just yours.
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Yes, Electrum, Sparrow and Bitcoin Core can do that easily.
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