SMB is controlling for small stocks. Small and thinly traded are not equivalent. For instance, for most of its history, Berkshire Hathaway was a large stock, but thinly traded (b/c of its high price).
There are a number of ways to handle liquidity risk. If you're looking to supplement a Fama-French regression, Pastor and Stambaugh (2003) uses order flow information to construct a liquidity factor. Both authors link to the factor data on their websites, so it may just be easier to do that.
Your point about using a dummy variable may not work well for a time series regression. This is because if you're identifying the periods where the stock is illiquid there might be other reasons why it is illiquid. I did see a paper by Bakaert et al that looked at something like the % of stocks that are illiquid, which might be similar to your dummy approach.
The benefit of the Pastor-Stambaugh approach is that it is in line with Fama-French in constructing portfolios from the most liquid and least liquid stocks and looking at the returns. You could also do something similar on a cross-sectional basis, but you may as well use the continuous data instead of converting it into discrete buckets.