It's easy enough to space out the process using Sparrow. You can simply enroll one UTXO now and wait for it to land in the new wallet, and then wait as long as you want before starting the process on the next UTXO. You don't have to enroll all your UTXOs in the process at the same time.
You can also freeze individual UTXOs in Sparrow which will pause their enrollment in free remixes for as long as you leave them frozen. Simply unfreeze them again and they will start to be remixed once again.
I am seeing two potential issues though...
1. When I did the process above, my wallet was hot. So, I had no issue. But, as I have said here:
https://bitcointalk.org/index.php?topic=5470024.msg63151565#msg63151565 if the wallet is airgapped, I think you can't generate the accounts. You need to turn your wallet into a hot wallet as long as this process goes.
2. Perhaps OP doesn't want to have equal size UTXOs in the end. If so, then I don't know how he can avoid it with Sparrow & Whirlpool. Let's say OP owns 20 UTXOs of variable sizes from 0.001
BTC to 0.1
BTC. OP will need to choose a coinjoin pool. Whatever size of pool he chooses (0.001
BTC, 0.01
BTC or 0.1
BTC) the final UTXOs will be of this specific size. There is a workaround, if OP chooses to use some UTXOs in one pool (say 0.1
BTC), then repeat the process for another pool etc. This will lead to UTXOs with sizes 0.001
BTC, 0.01
BTC or 0.1
BTC. So, if OP wants to maintain the same amounts for each UTXO (obviously minus the transaction fees), I am not sure he can.
He can avoid this size restriction with a WabiSabi coinjoin, you can create outputs with arbitrary values.