Forty years ago students of organic chemistry used to buy model kits to build molecular models much like you describe. The kit had lots of wooden spheres about 15 mm diameter, each painted a color to represent one type of atom. Each had small holes drilled into it, depending on which atom it was. Black balls had 4 holes placed along the axes of a tetrahedron to represent carbon. Hydrogens were white balls with one hole, Oxygen was red with two holes, Sulphur similar but was yellow, halogens were green with one hole, Nitrogen was blue with three holes again arranged like tetrahedral axes, etc. Then came the springs. They were steel springs about 25 mm long, about 2 mm diameter, with slightly tapered ends. To assemble you simply twisted the end of a spring into a hole - they were sized so the spring tightly screwed into the wood. Unscrewing took them apart. Some springs were a little longer and you could use two of them (bent into arcs) to join two atoms with adjacent holes to model a double bond, or three for a triple. Of course, the screwing together operation did not work quite right for the second spring, but just a tight push in would do it.
With this kit you could build whole molecules that were shaped properly, although the proportions of atomic diameters and bond lengths were not exactly right. The springs allowed bending and stretching motions to simulate molecular vibration modes, although sometimes the springs would detach when stressed, suggesting many molecules are fragile!
If you want a more robust version of that system, you could use metal balls and drill threaded holes in them, then make your springs with threaded metal caps on each end. What would be even better, though (thinking of the double bond situation) would be to use small ends and sockets that fasten together with a simple ¼ turn or less. If you wanted to be precise, you could make the balls of different diameters proportional to real atomic radii, and springs of different lengths to allow modeling interatomic distances correctly. I will warn you about an important factor, though. Although such a system will allow you to simulate the DIRECTIONS of vibrations (linear stretching, transverse bending, etc.) they will not model well the relative FREQUENCIES or AMPLITUDES of the vibrations. These aspects depend (in this mechanical model) on the spring force constants (or stiffness) in each direction, which depends on details like the type and size of wires used to make the springs.