It is quite possible that you have identified a suitable FUNCTIONAL replacement transformer. However, since you did not actually identify it, we can't confirm whether is is really suitable.
There are many such transformers with "split windings". So, for example, you can connect the two primary windings in parallel for 110V or in series for 220V. And in a similar manner the two secondary windings can be used either in parallel (for half voltage, double current) or in series (for double voltage, half current), etc.
However, it sounds like your replacement transformer won't be a PHYSICAL replacement because it doesn't have the same "pinout" or even the same number of pins. And of course the exact size and spacing of the pins is also likely to be a mis-match. In that case, you could hot-glue the transformer upside-down and run wires from the pins down to the board pads, etc.