And be sure to use a good filter for your shop vac, fine dust filter, ash filter, etc..There are and were many different brands of stove pipe,just buying a part without knowing what brand would not be smart.
Also be aware, as not in your manual(stove manufacturers want you to use a certified stove repair/cleaner), is a few things, once a year,or more, remove the combustion blower,and clean it and inside the cavity.Clean the room blower. On your stove,remove the pot assembly,clean and lube.
As winter is here, My recommendation would be-read manual well. I would buy some silicone sealer,perhaps some foil tape. Defiantly buy a flue brush kit. Remove the pipe from the stove, and from the wall,take outside and clean well. Reinstall and seal,at stove and wall. Before doing this, take out all removable panels,clean stove.You will be able to reach inside where the flue pipe goes on. Wacking with a mallet is also fine,I prefer a rubber one. It can knock loose stuck on chunks. Then I would see how it runs. All this is only a little bit of work, and if you seal the pipe properly, you may not have to remove it till summer. Also doesn't hurt to have a dryer cleaning brush,to stick in places. Strong shop vac., brushes and sealer would be my purchases today. Tape if you think you need it.
That's my 2 cents. A little bit of proper work,and see if stove functions well/ok.