Yes you can cast a spell with just a wand and words.
You can cast a spell with just words or even just your thoughts. Spells are just tools used to effect reality and cause something to happen.
While no spell is guaranteed they are usually flexible in materials, especially those of more simple design. You can normally find replacement materials to better suit your needs or abilities.
I would only suggest "going by the book" if you want to keep a traditional sense to it, or if you're creating a very specific potion, etc.
So as long as you keep the general idea and intent of the spell you should be fine.
And do feel free to explore your options and tweak the spells you use to better suit you/your own style.
lol This is why we often suggest you write your own spells, because it's just easier. ;)