Yggdrasil is right about the point - what should dissolve in nitric, when filter papers came from hydrometallurgical processing ? There is not much to be dissolved with nitric alone - you dissolve it beforehand, on the filters (if nicely washed), only insoluble portion is retained, that is most of the times AgCl, small gold particles and insoluble tin compounds + other ceramic/plastic/miscell junk.
Wet route for filter papers is doable, just you need to boil it for some time in AR to disintegrate the paper to cellulose sludge. Drawback of this method is - recovery of silver is practically impossible - unless you opt for ammonia leaching of the cellulose/whatever/AgCl/tin oxohydroxides/junk sludge
Not pleasant at all. But it will certainly work.
Personally, I incinerate them. Blend the papers, or press them that way they are not completely loose, but also not tightly hammered together - to allow gasses to escape and simultaneously saving the space in the pot you are using. It is wise to layer the papers with sodium carbonate - to help reduce AgCl to metallic silver (AgCl vaporize easily and melts just above 450°C). No reducers are needed as you have plentiful of carbonaceous material - which will easily reduce all metals down to zinc
Cover the pot with preferentially mineral wool and start heating very slowly - to the point you dry up the charge and it start slowly smoking. Light up the smoke and continue till you reach around 500°C (starting to see some dull red). If the smoke/flame is no longer going out of vessel, put the heatgun/torch aside and carefully open up the container. There should be carbon residue with all the ashes and stuff. There comes a fun part
Now, you need to burn all of the carbon from the residue. So in cheap DIY setup holding the temperature above 500°C in open container with VERY CAREFUL stirring of the carbon/ashes, till they come nicely greyish coloured and nothing is burning inside when swirled with steel or graphite rod - no sparkles of unburnt carbon emerge. Be gentle, residue is often very dusty and "floaty", with hot air currents tend to "fly out" the material form the pot. Depending on the ammount of paper, this coul take few minutes to few hours.
When you are left with thoroughly burnt ashy residue, now you have two options. Hydro or pyro processing. As the composition of this material is most of the times quite complex, you need to preferentially decide on what to do - based on what you have thrown into the container with filter papers
Main problem now is tin - it is all reduced down to metallic form now. So if you ever put the metastannic filters into the pot, you will have awful lot of tin inside. If you try to smelt this in graphite, you will obtain high tin alloy and that is painful to process ba any means. If you want to smelt it in clay, good luck with fluxing the SnO2 out. Better go with drilled magnesia brick and very basic NaOH or sodium carbonate flux, maybe with additions of nitrate to oxidize the base metals from the melt to the slag. But Air/better oxygen will also accomplish this conveniently
For hydro treatment of the ashes, it is wise crank up the temperature to around 600°C (good IR thermometers can reliably measure this) and hold for hour or two. With plenty of carbonate in the charge, all AgCl would be reduced to elemental silver by now, and the residue would stay porous. If you then take this residue and suspend it in water, all NaCl and Na2CO3 will dissolve, leaving all other junk from tin, and elemental silver together with gold in easy to filter form. But you need to reliably hold that temperature and DO NOT PASS THE 650°C. Otherwise NaCl will start to cake the residue to rock like structure and game over to the easy leaching
This process was developed by Wasyl Kunda, and it is used to convert AgCl to metallic silver on industrial scale.
Then you go from there, NOW apply nitric acid to dissolve the silver, and what is left is leached with AR to recover possible gold present
Processing multicomponent, full of junk, full of organic mixtures like filter papers is often quite PITA. I personally do it in bulk, when I accumulate few L bucket full of them, otherwise not worth it
Also, think about what you are adding into the container, have separate ones for silver, gold and PGMs and try to add as little junk as possible. Not all filter papers hold values and need to be added as "dead mass" to the pot.
It is said that "miligram to miligram, it all counts", but you will remember that phrase when you will be incinerating the carbon from filters for third hour in row and not nearly done
or going through washing of cellulose sludge from filter papers leaching, willing to sacrifice hundreds of miligrams of that same gold just to stop this suffering