Generally, it can be shortened for very commonly used expressions coming after the ~て form if they begin with another vowel (except u for various reasons, unless someone wants to prove me wrong), it can be shortened. Thus the forms you have written are acceptable, and possibly even more common in some contexts. Here are some more situations in which this happens concerning the ~て form:
~てあげる > ~たげる, e.g. してあげる would become したげる.
~ておる > ~とる, e.g. しておる would become しとる (you wouldn't hear this in modern standard Japanese; it happens in some dialects that still use おる rather than いる, but other than that it sounds ridiculously silly in standard Japanese. You might see it in anime and such, though.)
And of course, it is grammatical to use the polite ~ます forms in any of these situations.