Are all lithium ion batteries rechargeable?

I have a Sonicare toothbrush that died and I have cracked it open and am replacing the batteries in it. The originals were AA Ni-Cads but I would rather replace them with litiums. Will any lithium AA’s do it or do I need specifically rechargeables? Anyone see any problem with replacing Ni_cads with litiums? Is it safe to assume the charging mechanism in the toothbrush or the batteries will regulate the charging? Thanks.