Adding a smoky flavour without adding spiciness
Depending on what food you are trying to imbue with a smoky flavour, you have multiple options. I here focus on methods that will just give you a smoke flavour, rather than smoked ingredients.


Actually smoking the food seems an obvious suggestion. The internet will suggest any number of ways to set up a smoker at home, although you might not want to go through the effort or have to deal with the smoke.
Cold smoking is often done with cured meats and fish. As the name suggests, this is smoking (actual smoke from actual fire), but without the heat, often accomplished by creating some distance between the fire and the food, and having the smoke travel from the former to the latter. This guide seems quite comprehensive, including some ideas for a home setup. Cold smoking has similar drawbacks to hot smoking.
Some companies make 'smoke guns' such as this one by Breville/Sage, that accomplish the idea of a cold smoker on a much smaller scale. Thus, no need for elaborate setups, nor the risk of smoking up your whole house.
Finally, you can look for ingredients or additives that give you a smoky flavour. Liquid smoke is reasonably common. I have also seen powdered versions of this.