Having a phone "unlocked" is a software thing, they just plug it into a PC & run some software. This process is done all the time by 2nd hand phone dealers as they make their business on buying & selling phones & they have to make sure that they can be used by any network. If you have the cables, the patience, the know how & google you could do it yourself, this is why I suggested a 2nd hand dealer, they know exactly what to do & do it often.
The risk is minimal, & it is much quicker (& cheaper) than asking your old network for an unlock code - trust me I went down that road as well.
"An intelligent man is sometimes forced to be drunk to spend time with his fools."
Hemingway