Replacing my hhd with a ssd

So my Mid-2012 MacBook pro 13" has a 500gb HHD in it. I want to swap it out for SSD

but I want to transfer all my files over.

Now I know the best thing to do is to back my mac up with time machine to an external hard drive. However I do not have one and wouldn't really like to go out and buy one just for this. If i connected my HHD to a SATA to USB adaptor and then plugged it into the MacBook with its SSD inside could I transfer the files that way? I only have 60gb of information on the HHD so it shouldn't take forever to transfer over USB 2.0 speed.

would that way work or do I really just need to get an external hard drive?