Your basic idea is correct. Testing equivalence (or perhaps more common, in clinical applications, non-inferiority) of survival curves is covered nicely in this freely available review.
If your data satisfy the proportional hazards assumption for Cox regression, then you can test whether the confidence interval for the ratio of two hazard ratios (or the difference between their Cox regression coefficients) falls completely within the equivalence region that you have set. Quoting from the above review:
One could conclude noninferiority if the (1 − 2α) level confidence interval for the relative risk is entirely below γ0. Similarly, one could conclude equivalence if the (1 − 2α) level confidence interval is entirely between 1/γ0 and γ0.
Here, $\alpha$ is the choice for Type I error rate and $\gamma 0$ is the ratio of hazard ratios deemed acceptable for non-inferiority. Should your data not satisfy the proportional hazards assumption, the cited review covers how to test for non-inferiority or equivalence at specific time points.
Perhaps even more important to consider is whether you will have enough power to provide a useful test of equivalence. Survival data sets with small numbers of events can have very wide confidence intervals for hazard ratios, so that there is a risk of deeming 2 survival curves "equivalent" only if you are willing to accept a very wide equivalence region. Think carefully about how you or others will apply your findings of statistical equivalence.