Identifying a Positive or Neutral Ligand Inside Coordination Sphere?
Books have been written on the topic of whether a certain nitrosyl ligand is the nitrosyl cation, the nitrosyl radical or — you forgot this one — the nitrosyl anion $\ce{NO-}$. This ligand is termed a non-innocent ligand, meaning we cannot just look at it and tell what it is.

You asked for an answer that does not require IR or Raman spectroscopy. Well sadly, that means one has to resort to something even more exotic such as Mössbauer spectroscopy and ESR techniques. If you get lucky, a crystal structure may also help. Because the only chances we have to somewhat determine what we are dealing with are answers to the questions:


what is the $\ce{NO}$ bond length?
what is the $\ce{M-N-O}$ angle?
what is the spectroscopic oxidation state of the central metal (not the formal one)?
what is the count of unpaired spins?


One of the most obvious data points is the bond angle. A nitrosyl cation will typically only coordinate in a practically linear matter with an angle of $\approx 180^\circ$ while the nitrosyl anion will typically coordinate in a ‘bent’ manner with an angle of $\approx 120^\circ$. However, we also have the nitrosyl radical which has been shown to adopt both bond angles so we just lost our key piece of evidence.

Even using ESR to determine the spin state (i.e. number of unpaired electrons) can be inconclusive. Taking the related example of the binding of oxygen to haemoglobin, the current consensus accepts a structure that does not immediately conform to the observed spin of $S = 0$. The answer here is antiferromagnetic coupling that keeps to spins antialigned even though they could also not couple and observe Hund’s rule.

Thus, without a plethora of experiments you cannot determine in which state non-innocent ligands such as nitrosyl, dioxygen (which can be $\ce{O2, O2^.-}$ or $\ce{O2^2-}$ etc. bond to the metal. You may want to look at the related question on the electronic structure of $\ce{[Fe(H2O)5(NO)]^2+}$ for which I went through the trouble of actually looking up literature.

Because the oxidation state of iron and nitrosyl are so unclear, a curly bracket notation has been suggested. In this case, we would be dealing with $\ce{\{FeNO\}^6}$ (if I did the maths correctly).

Thankfully, you can always name these compounds by IUPAC nomenclature. Because IUPAC nomenclature desires to allow naming even when the actual electronic structure is unknown, it has defined nitrosyl to always be a neutral three-electron donor for nomenclature purposes. Thus, we would be able to call the complex you are interested in disodium pentacyanidonitrosyliron(III).