To be perfectly honest, as soon as you say "I want to practice techniques for one weapon by using a different one" you should understand that this will probably not result in a particularly rewarding experience. That's not to say you can't gain some facility by carefully practising with epees (or pieces of dowel for that matter) but it will be increasingly hard as you speed up your techniques and the instinct to use the sword as it was designed - as an epee - will always be there. That's not to say "don't do it", but do keep your expectations appropriately low.
To compare an epee to a rapier it's important to understand that an epee is typically less than half the weight of a rapier (less than 0.5kg for most epees compared to 1.0 to 1.6kg for a rapier). Even with the modern preference for practice weapons that are on the lighter end of the scale, an epee's weight is still significantly lower than a modern practice rapier. Epees also tend to be somewhat on the shorter side of historical weapons though not completely beyond the realms of possibility.
A couple of historical examples that are particularly light and moderately short:
http://wallacelive.wallacecollection.org/eMuseumPlus?service=ExternalInterface&module=collection&objectId=61148&viewType=detailViewhttp://wallacelive.wallacecollection.org/eMuseumPlus?service=ExternalInterface&module=collection&objectId=61159&viewType=detailViewA513 is particularly interesting in completely abandoning the typical rapier hilt but retaining the characteristic blade - and it is very light. I would love to know how that one feels in the hand!
http://wallacelive.wallacecollection.org/eMuseumPlus?service=ExternalInterface&module=collection&objectId=61006&viewType=detailViewIn looking for the least inappropriate period to study, it appears that in the time that the rapier was popular there was a noticeable trend away from the heavier weapons at the start of the period to lighter weapons at the end. Longer blades were more common in the middle period, with shorter ones found in both early and late use. There was, however, a significant influence of fashion which made for quite a mix throughout the period. It can also be difficult today to determine whether a particular historical sword was well suited for use in the manner described in a particular historical text (or, indeed, for use as a weapon at all) even if they are both dated to the same period.
Modern HEMA rapier practice tends to focus on sources across the span of about a hundred years from the latter half of the 1500s through to the middle of 1600s, but with your (very) light and (moderately) short epee, I would suggest that you look at sources from the periods slightly after that - 1650 onwards, perhaps. It should be noted that the period is one of transition, with some texts moving distinctly towards smallsword (a fine weapon in its own right), and others retaining and refining the rapier tradition (particularly in the Italian schools). Alternatively, accept that an epee isn't going to be a perfect facsimile anyway and just go with whatever appeals.
For books, Guy Windsor's The Duellist's Companion is the best generic rapier work that I'm aware of. Being a generic text it will obviously make no-one completely happy, but it's a good place for a begineer to start (I am little more than a beginner myself, so take that advice as you will). For period sources I am fond of Ken Mondschein's Agrippa translation - while from the earliest days of rapier the logic still holds true. The illustrations to be found in Capo Ferro's Gran Simulacro are superb, though the language can be a bit impenetrable at times even with the best efforts of the translators. Tom Leoni's Giganti translation is a clear and easy read. The only later period work I can think of off the top of my head is Reinier's Bruchius translation, which I confess I haven't actually read yet (though it is on the list):
http://www.bruchius.com/Eng/bruchiuseng.htmlGlyn