Yes, you can, hotspot icon is controlled by the faqbot-hotspot-container class of CSS which can be modified by proving the new code add after the widget code.
Sample code
<span style="font-family:arial,helvetica,sans-serif"><span style="font-size:14px"><style> </span>
<span style="font-size:14px">.faqbot-hotspot-container {
width:15px;
height:15px;
background:url(<Your new image url for hotspot>) no-repeat;
filter:invert(0);
}
@keyframes faqbot-hotspot-container { </span></span>
0% {-moz-box-shadow:0 0 0 0 rgba(26,115,232, 0.4);box-shadow:0 0 0 0 rgba(26,115,232, 0.7);}
70% {-moz-box-shadow:0 0 0 10px rgba(26,115,232, 0);box-shadow:0 0 0 10px rgba(26,115,232, 0);}
100% {-moz-box-shadow:0 0 0 0 rgba(26,115,232, 0);box-shadow:0 0 0 0 rgba(26,115,232, 0);}
}
// Just change the pulsating effect to new color as per need. in the example its chosen as 26,115,232.
</style>