Battery replacement for 5th Gen iPod, 30GB, Model A1136

I need to replace the battery of the captioned iPod 5th Gen. which should be part no. 616-0229 30GB , 3.7V, 580mAh but the batteries I find available in the market are part no. 616-0229 30GB, 3.7V, 650mAh which are used for the iPods Classic Gen 6th and 7th 80GB 120GB 160GB.

Considering that part no. is the same I guess that battery fits in the compartment and it is only the bigger capacity, so giving longer playing time.

My doubts and questions are: can I use this 650mAh Without harm to iPod?

thank you