I have a Burham like this too- it is a primitive but effective little SE. I actually have been shaving with it a lot in the past few months. It came with a spineless SE blade (which of course was no longer usable) so I loaded it with a Feather Spineless that I use with my Valets. Now many B&Ber's will tell you just to pull the spine off a regular SE blade- and that looks easy to do- even a youtube video available (I think), but I ordered the Feather Spineless some time ago and have been using those quite happily- not cheap but they are shaped perfectly for this razor and the Valets.
The razor you have is not exactly in pristine condition- if you can clean it up, it may be worth the spineless Feathers. I like the shave that I get with it so much that I have been thinking I may do a review of it on the Wiki if nobody has reviewed it yet. Guess I ought check that but something tells me that it has not been reviewed-- it is so basic and not the kind of razor that most people would wax eloquently about--- but I will if I get the time!