Any battery of the correct nominal voltage and physical size is likely to be perfectly usable. Any concern would centre on quality and at that the durability would be the issue. Rechargeables fail by holding charge for shorter and shorter periods and/or not reaching full voltage level. Buy and try out, I suggest.
I suspect cheap rechargables will be NiCd, which suffer from memory loss; in other words, if you don't let them go completely flat before you recharge them they lose capacity. Since telephones are normally put back int their charger when you finish a call, so are constantly being charged without going flat, NiCds won't be suitable. You need NiMH rechargables.
I'm disillusioned with pricey rechargeables, I don’t think I'd want to buy/use cheap ones. I reckon you’d be forever having to recharge every five minutes. I would hope they were safe though.
KARL is correct...you can't get NiCd batteries now. The cheapo ones from Poundland are NiMH...the only disadvantage is that they are low capacity ie hold less power, so don't last as long between charges.