The best way to avoid being rushed is to prepare before the appointment. Separate the strongest cards, take photos, know approximate recent sold comps for highlights, and decide which items you are not ready to sell. Use the card shop directory to find a shop that matches the collection, then call and ask for a buying appointment rather than walking in during a busy event. A scheduled buyer is more likely to give the collection enough attention.
At the shop, ask for the process before opening every box. Will they review while you wait, hold the collection with a receipt, or make an offer only on selected cards? The selling collection guide and card shop buylist guide show what terms to clarify. It is acceptable to pause, ask for a written summary, or leave with your cards. Pressure is not proof of a good deal. A clear process protects both the seller and the shop.