Essentially I have a seed that I want to get rid off so I generated a new one. I have two desktop wallets open on different computers (wallets "A" and "B"). Wallet A is using the old seed and Wallet B is using the new seed. The way I move funds is in several transactions from the old seed - Wallet "A" to a newly generated and attached to tangle addresses (every time a new one) on the new seed Wallet "B". Is this the right way to do it?
Sergey, there should be no serious risk.
Here is a step by step process:
1) On Wallet B, generate a new address.
2) Once it is generated, send that address to the computer with Wallet A, via email or otherwise. You are at no risk publically sharing the address.
3) In Wallet A, go to the send tab and send the amount of IOTA you want to send to that address.
4) Wait for your transaction to confirm. Do not try to submit more send requests.
5) IOTA should (hopefully quickly) confirm in the new seed wallet.
There is no risk to the above procedure assuming you do not attempt to double spend from wallet A.