Why is Ag+ a soft acid?
According to HSAB theory, Soft Acids have:

large atomic/ionic radius; 

low or zero oxidation state bonding;

high polarizability;

low electronegativity.

The ion $\ce{Ag+}$ satisfies all the aforementioned properties. 
I don't agree with you when you say it is anomalously small due to high nuclear charge and poor shielding by the d-orbitals. The effective nuclear charge has nothing to do here.

According to http://www.webelements.com/silver/atom_sizes.html: The radius of this ion is $114\ \mathrm{pm}$ when it's in 4-coordinate, tetrahedral geometry and it's $116\ \mathrm{pm}$ when  it's 4-coordinate, square-planar geometry. Please just compare these radii with the radius of  $\ce{Al^3+}$ ion : $53.5\ \mathrm{pm}$ which is considered as a hard acid.
I hope it's clear now!