You've posed a tough question. As far as I know, there is only one composition of J.C.Wodeyar in kalyANavasanta - srIranganatham - composed on the deity at Biligiri rangana beTTA - now the site of a tiger reserve.
This one is also supposed to be his last composition. See here
. I used to think that there are only the 94 compositions given by Vasudevacarya and tiTTE kRSNayyangar; and that there was no repetition of rAgas. So if we go by the idea that JCW composed a unique song in each rAga he handled, it is unlikely that SrivENkaTEsam is by him [although he has used the term guruguha in many of his songs]
However in the last couple of years, a few other kRtis have been unearthed; in the rAgas nAdabrahma, gItapriya (the vENkaTamakhin cognate of latAngi)and in sarasAngI
. The last is surprising, since this seems to be a rAga in which he has two compositions.