Possible to weaken single-slit diffraction? Without changing the source of the waves or width of the slit, is it possible to make the electromagnetic waves passing a small slit spread less by changing some other aspects of the slit such as surface material or border geometry?
 A: No.  The types of modifications you suggest can make small, practically undetectable, changes to the shape of the transverse intensity profile, but not the divergence angle.
I'm assuming here that when you say "border geometry" you mean the details of the edges:  rounded, chamfered, bezeled, sharp, ... without changing the size or shape of the slit.
A: One possible thing you can do is place another single-slit after the first single-slit to block the peripheral fringes and let only the middle fringe through. 
The single-slit creates its own diffraction pattern as seen here and here. The trick I'm suggesting here is to block the bright spots/fringes to the sides using another slit. Now, there would indeed be a diffraction effect from the second slit, but because most of the light of the middle spot goes through the middle of the slit, the diffraction effect would be small/negligible. Hence, you suppress some of the diffraction effects of the first slit.

You asked about whether a single-slit with huge thickness can achieve the same thing, and the answer is no. 
The problem is that the trick relies on you to create the single-slit pattern first, and then have parts of it get blocked.
When you let light from a single-slit, there is something called the Fresnel regime and the Fraunhofer regime. The Fresnel case has to do with the pattern formed when you're close to the slit. The Fraunhofer case has to do when you're far away from the slit, and that is the pattern I have linked above. 
The thing is, the Fraunhofer pattern needs space before it begins to form, so you need light to go unimpeded for some distance (as far as I understand). Hence a single-slit with thick material wouldn't work, because it wouldn't let the Fraunhofer pattern to form for the suggested trick to work.
Again, I don't know if this is what you're looking for. If not, then I would say garyp's answer is correct.
