What you will need is an SCR that is phase angle triggered. Simple versions of these suitable for lighting control are available in an integrated unit from various manufacturers.
Here is one I have used successfully for controlling an industrail incandescent load. They are not very expensive, but you are looking at about double the cost of a conventional dimmer switch.
https://www.gavazzionline.com/images/RM1EAAdatasheet.pdf
I know you can get them from Newark Electronics, maybe Allied has them as well.