All you need to do is
disable the proxy, and make the adjustment (I suggest log deleter v4). Doing it at the source will slow down the bust; but you'll also have to do the same at your target bank. Afterwards, wipe your tracks at InterNIC. If you're quick enough, you can go Bank 1 transfer then wipe → Bank 2 wipe → InterNIC wipe within a window of 90 seconds.
If you can't bypass proxy (don't have v5 bypasser or lack the means to use it), you can do like I do and before you make the transfer, first break the password, and log out and clean your tracks, log back in, reuse the password you got, and you're 'legally' inside the bank account. get your transaction ready, and before sending off, proxy has it's hold here, and if you lack bypassers, get all the info ready for sending before you crack the proxy. When you feel safe to send, hit 'GO' on the proxy disable program (must be v5 to work; cheap and easy enough to get), it will take it's time, depending on CPU power. I suggest having at least a 200; 2 200 CPUs are better if you have the +1 CPU board to be safer. The process will take between 15-30 seconds to crack. Provided enough bounces and a quick enough CPU, this shouldn't be too much of an issue; racing for bank 2 should be.
Here's what I did with my game. Default/Level 1 rig maxed out. Setup transfer account, started proxy v5 disable, after 10 seconds, I got pinged a notice that I have between 50-80 seconds left before traced, proxy has broke through, 1400000 Cr sent to my Uplink Bank account, just as immediately as I got confirmation (40 seconds left), I jumped straight for statements, delete most recent log, logout ASAFP. Bank 1 safe with 35 seconds to spare.
Bank 2, similar stats, except I started the proxy disable on the password screen as soon as it appeared, similar trace notice/time shown, with (again) similar time remaining, I managed to clear out the receiving end outstanding statement. My bank tracks are covered. Onward to InterNIC; usual cleanup routine. 30 in-game seconds later, I am promoted in rank 4-fold, and I have more than enough cash to replace my TRINITY rig (+ maxing out all hard and software) at least 3 times over.
All this with essentially the POS rig you start with (although maxed out compatible hardware-wise to ensure passage).
* Itnetlolor takes a bow