Is it okay to sacrifice exact country flag designs in favor of aesthetics? Is this okay?
Yes, but there are some cautions to observe.
Wikipedia's webpage on Vexillography explains:
"Vexillographers face the necessity for the design to be manufactured (and often mass-produced) into or onto a piece of cloth, which will subsequently be hoisted aloft in the outdoors to represent an organization, individual, idea, or group. In this respect, flag design departs considerably from logo design: logos are predominantly still images suitable for reading off a page, screen, or billboard; while flags are alternately draped and fluttering images - visible from a variety of distances and angles (including the reverse). The prevalence of simple bold colors and shapes in flag design attests to these practical issues.
Certain cultures prescribe the proper design of their own flags, through heraldic or other authoritative systems. Prescription may be based on religious principles: see, for example, Islamic flags. Vexillographers have begun to articulate design principles, such as those jointly published by the North American Vexillological Association and the Flag Institute in their Guiding Principles of Flag Design.
There is a solution, use a simplified (low resolution) design and place the countries TLD letters on it (see below). Reading about the history of the country's flag is a difficult and lengthy task when done for every country. Where resolution is very limited one could use two black letters on a white background with a rollover or clickable link taking you to a much higher resolution version.
These flags may look nicer, but is this in violation of the terms of how flags should be used in general? Do any countries have rules on how their flags can be represented and how strictly such a representation must follow the source design?
Whether or not something is "OK" depends upon the individual making the judgement. Some countries have specific laws regarding their flag while others have none, in some cases it's offensive to a religion to make certain changes. If you want to be polite use their design, if you plan on selling nothing there and never visiting you may have a bit more freedom. Offending a large country with many potential customers makes poor business sense, offending smaller countries ranges from simple bullying to actions seen as much worse.
If you are attempting to differentiate countries by their flag it's important to retain enough detail to distinguish between two countries where that is possible, in some cases that is extremely difficult.
The Internet website WorldStandards.EU lists all the top level domains for all countries. By drawing the flag using a civil flag design (see below) and putting two letters on each flag there will be a clear distinction between every country.
The North American Vexillological Association has a webpage: "Building a Flag Library" which lists books that can be consulted to aid in flag design.
The website "Flags of the World" (the Internet’s largest site devoted to vexillology (the study of flags). With more than 67,000 pages about flags and view more than 136,000 images of flags of countries) has a FAQ question: "I saw a flag similar to the one you describe for a certain country, but it had a coat of arms/no coat of arms in the middle. What was it?".
Many countries with flags charged with a coat of arms use that version as a state flag, but remove the coat of arms to make an easier to reproduce civil flag for their citizens. Examples include Spain and Ecuador.
Their are simplified versions of some of the more complicated flags available. How the particular country feels about you using their flag for profit is another matter.
It would be difficult to argue that you could not reproduce a maritime courtesy flag. These are flown on vessels visiting another country as a sign of respect.
See also this question on Politics.SE: "Are there any restrictions on what a national flag should look like?".