Generally speaking, yes, but there are a few things to keep in mind.
Are the essential oils part of the function?
In something like tiger balm or a tingly mint cooling concoction the essential oils are part of the core function of the product—don’t change them.
If it’s a lip product
Make sure you are using a lip-safe flavor oil, not a fragrance oil.
What is the maximum usage level for the fragrance oil you want to use?
Find out and make sure you stay within those maximum levels mentioned on label.
If it’s solubilized
If the the fragrance/essential oil in the original recipe was solubilized into a mostly watery concoction using a solubilizer (i.e., polysorbate 80 etc.), using a new fragrance or essential oil may necessitate a different amount of solubilizer to ensure everything stays properly solubilized (yes, even if the weight stays the same). This is something you will need to determine yourself through experimentation.
Want to leave out the essential oils entirely?
As long as they’re not part of the integral function of the recipe (see above), go for it—just be sure to replace the lost amount with a liquid oil or water, depending on the recipe. Oil is the preferred replacement medium, but if it’s a recipe that is almost entirely water (say, a toner with a small amount of essential oils solubilized into an otherwise water-based product) you can eliminate both the essential oils and the solubilizer and replace them with more water.