Lelouch and Nunnally being sent to Japan as Hostages was itself another ploy. In Season 2 when Charles is explaining everything to Lelouch when they are trapped in the Sword of Akasha he revealed that he sent them away to protect them for V.V who had already murdered Marianne.
Also at the start of the series we see C.C watching a young Lelouch and Suzaku probably before the war so given the connection Marianne had with C.C during the series it's possible C.C (before being captured) was sent by Marianne to look out for her children.
Prior the start of the War Britannia haddn't fully developed their Knightmares which was one of the key pieces of technology which gave Britannia an edge
However, when Britannia finally developed its Knightmare Frames fleet and decided to invade Japan to seize control of the Sakuradite mines, consequently discarding Lelouch's use as a diplomatic tool
Source: Lelouch vi Britannia - Character Outline (2nd Paragraph)
This means executing them would have no merit. remember also that Lelouch had forfeited his claim to the Throne and before doing this the background chatter by the Nobles talked about them being lucky if Nunnally could be married off for political gain in her condition. their value as hostages were already much lower and Japan's main bargaining chip was their Sakuradite which, now with their Knightmares, Britannia could take by force and stop the other super powers from getting it.
Also i would think Suzaku and Todoh would have done something to save them if someone got the idea to punish Britannia by executing them (and i suspect at the start of the series were we see Lelouch vow to destroy Britannia it was Todoh who we see at the fire).
As for making Lelouch's and Nunnally's deaths known to be false this would probably just insult Britannia. the first thing that would be done if this happened was to denounce Japan's claims and because most Britannians look down on foreigners chances are that Charles would claim that Lelouch and Nunnally were impostors withother probably voicing their disgust that the Japanese have the audacity to use foreign commoners to pose as members of the Imperial Family.
Lets not forget that the heirs to the throne were fighting one another, while there are some would would want to protect Lelouch and Nunnally there are others who would use the war as a cover to kill them permanently removing them from the line of succession. weather the Japanese knew is or not doesn't matter as Lelouch would be opposed to it because it would be putting Nunnally in greater danger.