It depends on where the PC gets its audio from the radio, and where your speaker or headset gets its audio.
The internal speaker in your radio gets shut off whenever there is a plug in either the phone jack or the external speaker jack. The external speaker gets cut off by a plug in the phone jack. All three of them have their volume controlled by the radio's AF volume control.
I'm not familiar with the Rigblaster circuit arrangement, but I'm going to guess that it gets its audio from the external speaker or phone jack on the radio (doesn't much matter which), and that the way you monitor is by plugging an external speaker or a headset into the Rigblaster. The radio's AF volume control changes the level of the signal to your PC as well as to the speaker or headset.
If this is correct, the simplest solution is to plug an unwired phone plug into the Rigblaster's (not the radio's) headphone jack. That should cut off the external speaker output without affecting the audio to the sound card. However, maybe you want to monitor, but at a lower volume level than your sound card wants, in which case this won't work.
Some radios have a fixed level audio output. If yours does, and if you use this instead of the speaker or phone output, then neither the AF volume control nor plugging in an external speaker or headset into the radio will have any effect on the audio to your PC. You will have to control the audio level into your sound card using the computer's software volume control, but you can control the monitor level with the radio's volume control.
If your radio doesn't have such an output, you can still achieve the same result by plugging an audio amplifier into the Rigblaster instead of your speaker or headset. An audio filter box will do. You then use the radio's volume control to control the audio level to your sound card, and the volume control on the external box to control the level of the monitor signal. That's how my setup works (no Rigblaster; my sound card gets its audio from a fixed level output on an outboard AF filter box plugged into the external speaker jack on the radio).
Something I've thought of but haven't tried is to use an amplified computer speaker as the external speaker. These speakers have their own volume controls and mini phone jacks, so you could use the speaker's volume control to adjust the monitor level without cutting off the audio to the sound card.
Hope some of these ideas help.
73, Rich
VE3IAY