For transformer search DigiKey or some other parts distributer, in my country I found transformers in Comet company, also they provide datasheet for transformers, you can look in these PDFs:
Yes transformers have various dimensions according to their powers. Also check other manufacturers, maybe you will find low profile transformer. I think its better to by new fabricated and tested transformer then make at home.
You can find is PC PSU lots of small transformers, they can be easily dissasembled in hot boiling water. I extract and dissasemble about 1-2kg of these miniature and other sized transformers, but if there is fabricated for small money then this is right solution. Always you can make more devices with small effort.
If you find corresponding quality fabricated transformer for your specification, always go with this. Safety reason is just one of aspect for this. These days prices for this small transformer are not to high.
Check these small SMPS projects, voltage and currents can be adjusted to your needs, read description text :