In that case, do away with the busking box and speakers and record directly into the laptop using something like Cubase, GarageBand, Reaper etc. You can then process or add effects to the audio if needed or desired.
If you don't already have one, you will be best off using an audio interface to plug the mic into, which then sends the signal to the laptop.
Look for a cheap one from Tascam, M-Audio, Prosonus. These start from about £60 and nearly always come with a cut down (but very useable) version of the aforementioned software, known as Digital Audio Workstations or DAW's.
Your recordings will be a lot cleaner, although you will need to think about monitoring (how your dad will her the music and his voice). For this, you would use headphones, but if you don't want then seen in the video, use the in-ear variety.
When you have finished recording, you import the video into some video editing software (iMovie, Windows Movie Maker or Premier Elements will do) and you replace the camera sound with the audio recorded into the laptop (just export if from the DAW software as a WAV.
When setting your recording settings for the audio, choose 16 or 24-bit and 48KHz. 24-bit is preferred if the option exists in the DAW software.