Yes, changing over to flat wound strings on this type of instrument is fine. String tension is a function of string design/materials, given pitch, AND scale length. The factory tension specification is dependent upon one scale length (usually 34 inches) for the note specified. If your instrument has a different scale length then strings designed for 34" scale will have an altered tension when tuned to normal pitch.
When changing string type, or brand name, it is almost always necessary to adjust the tension rod (neck relief) and re-intonate the bridge.
On Acoustic Electric Basses (AEB) the bridge is often fixed (Ala acoustic guitar) so your options for intonating the bridge are none - to spending money with a luthier to re-slot and reposition the saddle(s). Thus it is important to install strings that intonate well with the fixed bridge position of your AEB.
If your AEB has an adjustable bridge you are fortunate, your options are much greater.
Firstly, I would get rid of the original round wound strings as soon as possible to avoid rutting the fingerboard.
The DeAddario EXPPBB170 Coated Phosphor Bronze Wound set has these tension specs. From
http://www.juststrings.com/dad-exppb170.html1st G .045 47.5
2nd D .065 55.7
3rd A .080 47.4
4th E .100 40.2
DeAddario Chromes are a good choice. They come in four tensions...
From
http://www.juststrings.com/daddarioelec ... romes.html
ECB80, ECB 81, ECB82, ECB84
According to the information at JustStrings, the ECB81 set is closest in tension and gauge to your existing set. HOWEVER, they are not exactly the same so you will still probably need to adjust your neck tensioning rod.
This set should also be fairly close regarding intonation. Most likely the intonation will be a bit different. On instruments without adjustable bridges it may be necessary to try several different strings sets until you find one that intonates well, thus avoiding expensive bridge modification. Use your ear. If a set just does not sound musical, or you cannot get used to finding notes in the higher regions of the fingerboard then it might be that the new strings are substantially different in intonation characteristic than the set for which your instrument was originally set up.
Just because the sets are by the same manufacturer does not guarantee that two different lines within that company will have similar intonation characteristics. Conversely, a set from a different company may have the exact intonation characteristic you need. You may have to experiment with various sets until you find the one that works well for you and your axe.
Your highest priority should be finding a string set that intonates well and sounds good. Tension is secondary as adjusting the neck tensioning rod(s) is usually an easy operation.
Adjusting the tensioning rod (neck relief) is an essential skill if you intend to be a master of your instrument. If I were in your shoes it would seem prudent to use this as an opportunity to get your feet wet doing neck adjustment to achieve your perfect neck relief. Acquire the tool required for tension rod adjustment, be sure to read up on the technique used in neck adjustment and relief. There are many sources available on the net as well as here on this site. It is possible to damage your instrument if you improperly adjust the tensioning rod, so please read up on it, and get some advice or help from a knowledgeable person should you be unsure of your ability to work with tools.
Try to find a fellow bassist with many sets of used strings. I never throw out my old strings and have boxes of various sets that are still in good shape. See if you can borrow an assortment of old strings and try different sets that might be good candidates.
Search FretlessBass.com for "strings", you will find some interesting reading and also some other contenders for your string choice.
Good luck, and welcome to the Fretless Bass community.