I agree with o_e_l_e_o.

The way I did it when I wanted to change was:

1. I sent some UTXOs separately in various times (1 utxo today, 1 two weeks later, 1 one minute later etc).
2. The rest of them I used o_e_l_e_o's process, it worked smoothly.

The only thing I don't like with this option (2) is that most of the coins will move from wallet A to B in in close moments of time.

Ιf this doesn't bother you, then follow his advice. It is the best you can get.