I plan on doing some wiring but the directions are asking for 1A 600v rectifier diodes. I could only get my hand on 1000v rectifier diodes and before I continue I want to make sure this is safe as if I wont cause a fire or a short or make something blow up.
In general, it is safe to be overly conservative with a component specification. If your design calls for 600V rated diodes, then using diodes rated for 1000V shouldn't hurt anything, all else begin equal.
However, you have only provided information for the voltage rating. If the 1000V diodes can't handle 1A of current, or are insufficient in some other area, you could still have issues.
The only situation in which you would not be able to increase the voltage rating (all other performance metrics being equal) would be if the circuit depends on the reverse breakdown behaviour of the diode. No* properly designed circuit, however, will rely on the reverse breakdown behaviour of a conventional diode.
*Note: there may be exceptions, but they will be exceedingly rare, and I can't think of any case where a Zener or avalanche diode wouldn't be a superior choice.
There is unlikely to be any negative consequences to doing this, just make sure they are big enough to handle the current. That rating is just the maximum reverse voltage they can take. More is better.
If they are recommending a specific part, you may want to look at some of the specs like reverse recovery time or forward voltage drop, but it almost certainly doesn't matter.