Can you set a DAW to use ASIO input and something else (laptop speakers for example) as the output?
No, it is not currently possible to use ASIO in a DAW as an input source, only, without using it as the output on Windows.
However, I have seen people claim ASIO4ALL let’s you mix devices in some DAWs.
On the Microsoft Windows, you can use ASIO4ALL to use an audio output that is different from the audio input. For example, in the following screenshot, ASIO4ALL is configured to use the Focusrite USB as input, and the Virtual Audio Cable as output:
Note that you have to check the device (e.g., "Virtual Audio Cable") in addition to the the in (or out) checkboxes for it to be enabled:
Also, it seems that one can only use 1 output at once (e.g., one can't send the output to both the "Virtual Audio Cable" and the speaker). To be confirmed.