The propper configuration for a wrist strap is not to connect it directly to ground but through a resistor to ground. You want to disipate the static on your body not simple discharge it. You do not want to have a constant path directly to ground, especially on yor wrist. There may be bad, very bad, consequences if you come in contact with the power mains with your other hand. Instead of getting a mild shock, you could easily get the total voltage from arm to arm with the current flowing through your chest. Most wrist straps have a 1M resistor incorporated. Commercial wrist straps, as a tool that will last a long time, are available at most electronic suppliers, computer stores selling upgrade parts and on-line for a resonable price. You will take care of the safety issues as well as having a comfortable sollution with the commercial wrist strap made of a elasticised fabric and the wire being a coiled cord with the resistor built in. It will likely cost you about what an Arduino would.
In a former job, I worked in electronics manufacturing and was responsible for the plant wide static control program. We required workers to wear static disipative smocks, wrist straps while seated, work at stations with anti-static surfaces or mats, wear heel straps or static dispative shoes on specially waxed floors while standing or moving product. Each person checked both their wrist strap and footwear at test stations when entering the production floor. Work surfaces, mats and floors were tested frequently to ensure the disipatve connections.
Static can cause immediate failure of parts and latent failure where the part fails at a later time.
Hope this helps. Ensure you take the propper steps for your own safety - don't connect yourself with a wire directly to ground!
tjmck