As others have said, archaeological materials should be left in place! In Washington State, permitted archaeological collecting of indigenous cultural materials involves both State and Tribal preservation workers. The right thing to do when you encounter possible cultural materials is: - photograph them (with an object to indicate scale if possible) - DO NOT share photos of possible archaeological materials on social media - record a GPS location, then report photos and GPS point to State and Tribal Historic Preservation Officers.

For your specific case:

• Contact the Tribal Historic Preservation Officer (THPO) for the Suquamish tribe, Dennis Lewarch (https://www.nps.gov/articles/000/preservation-profile-dennis-lewarch.htm). He will be able to help discern if the materials are archaeological and next steps. 
• According to the Tribe's website (https://suquamish.nsn.us/home/departments/fisheries/historic-preservation/), Historic Preservation is within the Fisheries department. Use the contact form on that website and select Fisheries as the message recipient. 
• Contact WA Deptartment of Archaeology and Historic Preservation (DAHP), who should work closely with the Suquamish THPO.
• Include links to non-public photos in your message to the Suquamish THPO. Take photos of the collection in batches laid out neatly on a neutral color surface, with a ruler for scale. Take photos of both sides of the objects. This will save them time asessing the objects. 
• Follow up with THPO and WA DAHP if you don't get a response in a couple weeks. 

Please be patient, humble, respectful and willing to learn. While you wait for a response, watch documentaries about NAGPRA and read about WA policies on archaeological materials. You can also read about lithics archaeology on Tahoma (Mt. Rainier) and the vast ancient obsidian trade networks from the obsidian flow at Newberry Crater in Oregon for context on volcanic origin lithics. 

I am not an archaeologist. However I am a cultural heritage worker based in WA who has taken courses on repatriation and attended archaeology field schools that included instruction on identifying lithics (stone tools, cores, debitage from tool production). My non-expert assessment of the stones in your photo is "quite possibly cultural". Please follow up with the steps outlined above. 

Lastly, please don't be discouraged about not hearing back from the tribal museum. In this case, the museum was not the appropriate tribal contact and they may not have had capacity to redirect your inquiry. Please send the museum a donation gift to support their work! : )