Closed analytical expressions for scattering intensity and other global structure factors are derived for a new solvable model of polydisperse sticky hard spheres. The starting point is the exact solution of the ''mean spherical approximation'' for hard core plus Yukawa potentials, in the limit of infinite amplitude and vanishing range of the attractive tail, with their product remaining constant. The choice of factorizable coupling (stickiness) parameters in the Yukawa term yields a simpler ''dyadic structure" in the Fourier transform of the Baxter factor correlation function q(ij)(r), with a remarkable simplification in all structure functions with respect to previous works. The effect of size and stickiness polydispersity is analyzed and numerical results are presented for two particular versions of the model: (i) when all polydisperse particles have a single, size-independent, stickiness parameter, and (ii) when the stickiness parameters are proportional to the diameters. The existence of two different regimes for the average structure factor, respectively above and below a generalized Boyle temperature which depends on size polydispersity, is recognized and discussed. Because of its analytic nature and simplicity, the model may be useful in the interpretation of small-angle scattering experimental data for polydisperse colloidal fluids of neutral particles with surface adhesion.